"Ground Zeroes" is the primary story mission of the game, and the only playable mission whose story connects to The Phantom Pain as part of the full "Metal Gear Solid V Experience". Your objective for this mission is to free Ricardo "Chico" Valenciano Libre and Paz Ortega Andrade from their imprisonment in Camp Omega, Cuba, and extract them via helicopter.
Rescue Chico and the POWs
You begin just outside the camp, in the south-west of the map. You can rescue either Chico or Paz first, but rescuing Paz first will result in the security around the area where Chico is being held being increased, so it's easiest to extract Chico first. Chico is being held in the old prison area to the south-east.
Begin by holding down 
to equip your binoculars, and use 
to look around. Press 
to adjust the zoom level. Just ahead of your starting location is a searchlight with a guard posted to it. To the left of the watchtower, on the ground, is the gate into the compound. There should be some guards standing around the gate talking. Zoom in on them, and focus on them for a moment, to mark them. Marking enemies makes their positions and movements appear on your map (available either via the tablet app, or by pressing 
), and allows you to track their locations even through walls. Move forward while avoiding the searchlight, and stick to the rocks to the south. Keep low to avoid making yourself obvious - press 
to crouch, or hold 
to enter the prone position and crawl. Follow the path, and you'll come out just below the watchtower, on the same level as the guard inside. This is a perfect vantage point from which to eliminate him. Hold 
to ready your weapon, move to aim, and press 
to fire. If you prefer, you can use first-person aiming by pressing (press again to switch back to over-the-shoulder view). First-person mode is best used while prone, which allows you to hold your weapon more steadily. You begin equipped with an automatic rifle, but if you prefer to dispose of enemies non-lethally, you also have a silenced tranquilliser gun to hand. Use 
to switch between weapons. 
equips your primary weapon (rifles, shotguns, and such), 
equips items (you begin with night-vision goggles, and can pick up empty magazines to throw and gain or draw away the enemy's attention), 
equips support weapons (such as grenades), and 
equips secondary weapons (one-handed weapons such as handguns). Press to equip the tranq gun, and put the guard to sleep. A headshot will kill/sedate him instantly. You should also note that your rifle comes equipped with a suppressor and flashlight. To equip/remove these, hold , select the rifle, and press 
to toggle the suppressor, and 
to toggle the flashlight. You should remove the suppressor when it's not needed, or if you get involved in full battles, in order to not wear it out too quickly. The flashlight is useful for seeking out enemies in dark locations, but can also give away your location if noticed.
when prompted to grab him and enter CQC mode. From here, you have three options. Press to slit his throat and kill him. Press again to strangle him into unconsciousness. Press 
to force him to speak - push 
to make him "spit it out", which may gain you useful intel such as enemy or target locations, or 
to make him "call 'em", which will make him try to call for help. Move while holding him to use him as a human shield (you will be unable to use your primary weapon).When the guard is dispatched, approach the gate, and push 
towards it to press yourself to it. This enables you to watch for guards on the other side of the fence. At some point an enemy vehicle will pass through the area, so ensure the area is clear before proceeding. Approach the gate and press when prompted to pick the lock. You can now enter the compound. Begin moving east. Use the walls, sandbags, and foliage to hide from patrolling guards, and mark them with your binoculars when you have the chance. If you're noticed, and need to get down flat quickly, press while moving to dive. This is useful for hiding among plants quickly if an enemy truck passes through the area. While hiding behind a wall or sandbags, Continue moving east while sticking to the walls to the south. Ahead of you is another watchtower with a guard. Avoid the searchlight, and approach the tower until you come to some sandbags. From here, you can press to prepare a Cover Attack, and to shoot, allowing you to take out the enemy while using the wall for protection. Be quick about it though, or the guard will spot you. If you prefer, you can continue moving south and approach the tower from behind. Press to climb the ladder, and approach the guard from behind, offering you a choice in neutralising him - CQC, or holding him up (draw your weapon while close enough). With another searchlight out of the way, continue following the wall around to the north, and take the path to the east. There will probably be a guard around here - silence him with your weapon of choice (it's probably too risky to get close and use CQC or hold-ups), and hide the body in the nearby shelter. Continue east to the prison area.
There will be guards posted outside and inside the actual prison area here, but luckily the searchlight is deactivated (unless you already rescued Paz). Use your binoculars to mark out the enemies' and prisoners' locations, and continue your approach along the walls and cliffs to the south. Keep an eye on the guard within the compound, as he's the most likely to spot you at the moment. Since the watchtower is abandoned, you can use it yourself to scan the surrounding area for enemies. This is a good chance to take stock of your enemies' current locations around the prison area. At some point, the guard patrolling inside the prison may choose to move outside of the compound. If he does, you can jump down from the tower and into the compound by pressing (be careful not to activate the searchlight). Make sure beforehand that the guards are behind the canvas on the northern fence, where they can't see you. Once inside, approach your target, Chico, who is in the north-easternmost cell, and press to pick the lock. During the cutscene, your attention will also be brought to the other prisoners in the camp. Rescuing these is optional, but required to obtain the highest ranking. For now, focus on Chico, and you can come back for the others later if you wish.
You should call in your helicopter as soon as the cutscene ends. If you have the tablet app, touch "Helicopter", and hold down on the white circle a little north-east of the prison. If not, press to open the iDroid, select "Helicopter", and select the landing zone to the north-east of the prison. Hold 
to pick up Chico. While carrying Chico, you cannot use your primary weapon, and cannot go prone. Proceed north-east, sticking to the cliffs (but be careful not to fall off!), and hiding behind the walls. Silence any guards you come across. If you need to drop Chico in order to equip your primary weapon, find a safe place to hide him, and hold . Head to the rendezvous point marked by the orange square. By now, Morpho should be arriving with the helicopter. When he lands, approach the helicopter and press to place Chico on the helicopter. If the enemy is in Alert Phase, they may spot the helicopter and attack it, so you'll need to work quickly to unload Chico (you may need to hide him in the nearby alcove in order to remove some of the enemies). With Chico safely extracted, you can now either return for the other prisoners (return to the prison area, rinse and repeat this paragraph four times), or proceed to rescuing Paz.
Rescue Paz and escape
After you unload Chico onto the helicopter, he will drop a cassette tape, which will begin to play automatically. From the cassette tape, you hear that Paz has been taken to an area where there is a flag, and a heliport. Head west and north from your landing area. At the junction, a guard will enter a truck and drive north. Wait until he leaves to proceed. As you head under the bridge, you'll hear a flag - you're heading in the right direction. Next is the heliport. Continue north, watching out for patrolling enemies. As you approach the north wall, Miller will contact you and inform you of the helipad to the west of here. Head west towards it, sticking to the northern wall and the barriers alongside it (along the way you may need to cross over to the area with the cargo boxes to maintain your cover). At the end of the north wall is a building which you can crawl under. Head north under it, and you'll come out near a drainage tunnel. Crawl through this (travelling westwards). When you emerge, continue west, sticking to the wall, and enter the red door in the northwest corner.
Inside the admin building, there is one guard patrolling the floor, and a surveillance camera on the north wall watching over the staircase. Sneak up on the guard from behind, and kill/tranquillise him with CQC after interrogating him. To avoid the camera (if you shoot it out, unlike in past MGS games security will notice that it's broken and raise an alert), hide behind the pile of pallets and wait for it to point away from you, then press to jump over the pallets, and run to the corner underneath the camera (watch out for any guards that may be coming up the stairs). Once the camera is facing away from you, run down the stairs (push 
to dash). Go straight ahead of here (south on the map). At the end of this area, Paz is being held in a cell. Press to pick the lock.
You must now escape with Paz. You have three choices of landing zone for your escape helicopter. One is immediately outside the admin building, but it is likely swarming with guards, and the security will increase further once they discover that Paz is missing. If you've removed all the guards in this area, though, it will be safe if you're quick enough. Another zone is south of here, but it's likely your worst option - you have to avoid two groups of guards (those outside the admin building, and those at the zone itself), and the guards around the zone itself will still have its full contingent. Lastly, there's the original zone from where you extracted Chico - it should have no guards, but it's quite a trek to get there with Paz on your back. If you're going for the first, call the chopper just before you exit the building. If you're going for the last and furthest away, wait until you're at the bridge to call it in.
Pick up Paz, and move for the staircase. Guards will be coming down from the upper levels now, so watch the area on the left as you pass. Avoid the camera again as you come up the stairs. Another guard will have been posted to the next area, and he will usually take the catwalk to your left, so you may want to travel underneath the catwalk instead. Exit while the guard is facing away from you.
If the area outside is clear of guards, and you called in your escape chopper, it should be arriving soon. Load Paz onto the chopper with , and shoot down any enemies that may try to attack you until you escape to victory and end the mission.
If you chose to go for the original landing zone, proceed eastward along the north wall, hiding behind the cargo boxes. At the end of the row of cargo boxes, a tank will be waiting. Avoid it the same as you did the camera. Retrace your steps back to the landing zone as quickly as you can, while ensuring as best you can that you aren't spotted by any guards. Call in your chopper while you're under the bridge. Get to the landing zone, and prepare for extraction.
Once the escape helicopter is clear of all enemies, and free to fly out of Camp Omega, your mission is complete.