StarCraft/Terran mission 3: Desperate Alliance

You don't have to attack anything in this mission: you simply have to survive. This isn't as easy as it sounds. You'll be facing air units for the first time, but really they're not very hard to kill. After you have a strong resource chain, fill up your existing bunkers with three Marines and one Firebat each. Then build two more on each base entrance as the mission progresses. As for unit production, you shouldn't really build Factories; all you can do with them in this mission is build Vultures, and they're not particularly useful. Instead, have two or three Barracks going, all producing Marines and Firebats.

Also, build two Missile Turrets in each base entrance. These and the bunkers' Marines will pretty much shred all Mutalisk attacks, but just in case they decide to go over the roof of the building protecting you, you should put at least 12 Marines on the roof (you can't build anything up there). Even if you think you've got enough defenses, keep building units. You might have 100+ supply worth of infantry in this mission: all the better for you!

For most of the 30 minutes, Zerg attacks are light. This is because they're saving up their forces for a final assault. With 2 minutes remaining on the counter, the Zerg will launch a massive attack. Expect a horde of more than 50 Zerglings and loads of Hydralisks and Mutalisks. This is exactly why you created as many units as you did. You should be fine, but if the defensive line is broken in a base entrance, lift off all buildings and move them in different directions on the map. This makes it impossible for Zerglings to do anything to them, and will buy you time. When the camera shifts to an edge on the map, your rescue has come.

If you want to reduce the number of bunkers that you have to build, then one strategy is to use what will become the foundation of your Terran defense as the game goes on - the Wall-In Chokepoint.
 * Addendum

What is the Choke-Point, you ask? What it means is that when you have a narrow gap that the enemy must go through, you build a line of supply depots to block it off. Behind that, you put your bunkers and missile turrets in clumps. The advantages are obvious; the Computer can not hit the bunkers directly without first attacking and destroying at least one supply depot to get through to them, while your guys (your marines, in any case) get to shoot and kill them).

Try this with this mission if you decide to play defensively. Build a line of supply depots blocking off each entrance. Behind it (meaning RIGHT behind them, so that they can hit the enemies), build a line of bunkers - at least two at each entrance will probably do it. Then put two clumps of three turrets at each entrance, meaning a four new turrets since the mission starts with two turrets at each entrance. Build a cluster of 3-4 turrets right next to your mineral patch, as well. With that defense in place, your base is next to impenetrable - just keep at least 2 SCVs near the choke points near the end of the mission, since you'll need to repair those structures (particularly the Supply Depots) immediately as they are damaged, and probably repair your SCVs as well. Pull the remaining marines off the walls, and keep them in your base to deal with random mutalisks.

Aggressive Method
There's a way to see some more action if you don't want to sit tight in your base. Although it's not necessary, you can actually attack the Zerg and prevent them from creating that huge army. This is not recommended for new players, simply because it can be very difficult to pull off. What you do is after filling up two bunkers at each base entrance, have three Barracks produce two to four full groups of Marines and one full group of Firebats. Also, upgrade Marine range and Infantry Armor and Weapons. Send this force north from the right entrance to take out the small outpost there, and basically mop up the Zerg bases. You might run into Sunken Colonies, which will kill Marines in only a couple shots, and you must focus all fire on these structures if you do. Keep producing units at your base in case this attack fails. Finally, if the attack force is not ready by minute 20 at the very latest, scrap the attack. The massive horde will pretty much be done, and all you do will be to enrage them.

If you can manage to wipe out the Hydralisk Den in the upper left hand corner, it should be easier to take out the base as they will no longer have Hydralisk reinforcements.

Alternate strategy 2
Although this can be difficult if this is your first time playing Starcraft, this strategy can be quite fun - even after they create the army.

What you need to do is get mining, immediately. Send your SCV over to the burning bunker to fix, but while that is going on, get building scvs. I recommend that you hotkey your command center on hotkey "0"; to do this, simply hold the "ctrl" button on your keyboard and press "0". From then on, when you click on "0", it will be as if you had click on your command center. Do this for your barrack(s) (you will be building two), and if you build it, your ComSat station.

Here's a trick with the "Aggressive Assault" strategy. Bring down all the random marines from the walls, and make sure your starting bunkers are full (4 marines each). Hotkey the gathered marines left under hotkey "1"; you can use them to help protect your base while you build the attack force. Continue building SCVs at your command center, and build a refinery and SCVs to mine it (you need the gas for firebats, and you MUST research the U-238 Range upgrade at your engineering bay). Keep building marines, then firebats when you are ready; ideally you want 2 marines for every 1 firebat, because the computer will use mutalisks (air units) in this mission, and only marines can hit them. When you get a force of 12 (all you can select), put them in a force group (meaning "hotkey them on to a number you can click quickly"), and keep building the next force group.

While this is going on, get your defenses ready. You don't need to build additional bunkers at the entrance if you pull off the attack successfully, so instead make sure they are filled with marines, and repaired regularly by SCVs. Build two missile turrets in a clump near your mineral patch, but make sure NOT to block off the path to the back minerals for your SCVS; that can really slow down your mining. On the top entrance to your base, build supply depots around the front of your bunker so that they form a wall one supply depot deep blocking off the enemies from hitting your bunker. Don't put the supply depots too far forward, otherwise the comps will attack them. Around your bunker, build at least two missile turrets, clumped together. At the south entrance, build two supply depots to force the enemy to go through a narrow passage, but DO NOT block off the entrance; this is where your guys will be leaving. Build a ComSat station at your main base (it's an attachment to your command center; click on the command center and you'll see the option to build it). You can use the Command Center to scan areas of the map, and you'll want this to figure out where the comp's structures are at (principally, the Hatchery).

When you have two mixed force groups of marines/firebats, take them out the south entrance, and using the "Attack" command, send them straight out from the entrance towards the north-center of the map. It helps if you built a ComSat station first to scan - that way, you can see what structures are where. Make sure to keep your force together; scattered marines and firebats are food for zerg. Once you have identified the Hatchery, use the Attack command, and send your forces at it (DON'T click on the Hatchery with it - they'll go straight for the Hatchery ignoring everything else. Click on an open area behind it, so that they attack everything on their way there.)

They will probably meet fierce resistance in the form of zerglings, hydralisks, and mutalisks, but the two force groups are pretty tough for this mission. Make sure while this is going on to continue building marines and firebats using the hotkeyed barracks back at your base; you'll probably need reinforcements to make sure your main force always has at least two force groups' worth of guys. An extra trick is to build a second force group and send it at zerg structures away from the hatchery, so that it will divide their forces.

Once you have destroyed the hatchery and surrounding structures in its "clump", the rest is mopping up. Using the ComSat station to scout, send your forces around using the Attack Command to kill what's left of the Zerg on the map. Then relax - you've effectively won this mission, and you can simply wait for the clock to run down.

You don't have to do the above; you can simply sit tight under massive defenses and wait out the clock. However, doing the above is good practice against the Zerg you will have to fight later in this campaign, since the Zerg both attack and produce new units. It's also good practice for both cordoning off chokepoints (the key to Terran defense), and using multiple production structures to build up forces of guys.