South Docks
You'll begin on the south pier of Liberty Island, equipped only with a Pistol, Riot Prod, and Medkit. Alex messages you through your infolink and tells you that your brother, Paul, is on his way to meet you on the pier. Move forward and you'll see a figure in a trenchcoat heading towards your direction: this is Paul, and a conversation will trigger as soon as he's near you.
Paul tells you that the NSF terrorist group has taken over the statue and has taken Gunther Hermann hostage, who is one of UNATCO's top agents. Paul also lets you choose an additional firearm in order to make your life easier: a sniper rifle, a GEP gun, or a mini-crossbow. It's up to you on what you want to choose, but remember that NSF mercenaries carry mini-crossbows and one of the terrorists near the front entrance has a sniper rifle. Once you're armed, Paul says that your primary objective is to locate and interrogate the NSF commander, and uploads you an image of him before the conversation ends. Once it does, look for a Crowbar among a stack of crates on the right-hand side and pick it up. You can use it to smash the two nearby wooden crates, in which you'll find a pair of Binoculars and a Lockpick.
Go down the staircase on the left that goes into the water to find a broken sharkcage. Inside the sharkcage are two other wooden crates, so smash them both to find a Multitool and a Bioelectric Cell; head back up after you get both of these items. You can talk to Corporal Collins, who gives you more information on Gunther, and you can talk to Paul two more times to uncover additional information. Keep heading down the dock to find some more wooden crates in the corner: destroy all of them in order to find 10mm Ammo, a Prod Charger, and some Darts. You can also pick up a Baton that's sitting on top of the wooden railing to the left.
Afterwards, proceed up the ramp and run to the left. If there's a guard stationed nearby, dispatch him; if not, hide in the left corner and wait for him to come, and then dispatch him. However, make sure the second guard is far away from the first so you don't have to deal with both of them at the same time (and so more guards aren't alerted). Now wait for the second guard to come around (he patrols on the right-hand path) and then take care of him. The method of elimination is up to you: you can kill them, knock them unconscious, or simply sneak by them. If you'd like to save ammo, you can alert the guards and then run back to the pier so Paul and the security bot make quick work of whoever comes by. These two guards will carry 10mm Ammo and a Knife, which is standard for most of the NSF enemies.
Once both guards are down, take the small metal crate and place it next to the large stack: jump on top and smash the wooden crate to find a Gas Grenade. Below you, you'll notice a small storage area that houses a medbot, but the door requires a certain amount of lockpicks, depending on your skill level. Keep going down the main path on the left, and eliminate the guard closest to you (be careful however, as he carries a mini-crossbow equipped with tranquilizer darts, which brings your health down faster). After he's down, you can search his body for a Mini-Crossbow. Now take care of the other guard that's not too far away; he carries some 10mm Ammo and a Knife.
On top of the nearby container, you'll notice a datacube, a Prod Charger, and a Pepper Spray Cartridge. Read the datacube to find out that the login is NSF001 and the password smashthestate. On the same path, follow the one that branches off and goes to the UNATCO headquarters (along the way you can find a Mini-Crossbow on the corpse or some Tranquilizer Darts if you already took the bow).
UNATCO HQ
At the entrance you'll find Tech Sergeant Kaplan, who triggers a conversation with you. You'll have to make a choice halfway through. Your choice will have a small effect: if you choose the first one, he'll give you the code (0451) to the shed next to the helipad, but he won't give you the code if you select the second option. Afterwards, he'll offer you some hardware: a Scope for 700 credits, some 10mm Ammo for 200 credits, or some Tranquilizer Darts for 60 credits.
When you're done talking to Kaplan, approach the green shed next to the helipad to find a Crowbar and a wooden crate which contains a Multitool. There's also a wooden crate that has a Lockpick inside that's behind the shed (you have to go through the small alleyway to the right). Punch in the code 0451 to open the door to find a Medkit on top of the machines and Tranquilizer Darts on the table. Underneath the table is a datacube which contains the information for the security terminal on the wall (the login is SATCOM and the password is UNATCO_001). Use the security terminal and use the information (or hack it) in order to unlock the nearby access door. Go back outside and into the access door to find a wooden crate which contains an EMP Grenade. Exit the UNATCO HQ and head back to the main path; from here, there's many different ways to get into the statue.
If you'd like to get in through the front doors, go to the "Going in Through the Front" section. If you want to go in the back way, proceed to the "The Back Way" section.