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You start out with the Green Beret inside a cell. Smash up the fellow who comes inside. Look out through the door. When the engineer has his back towards you, go out and knock him out as well. Take his cigarettes and stash him in the cell. Use the cigarettes to lure and beat up the next guy. Then take out the last guy in that area (and pick up the goodies from the crate nearby). Enter the cell next door, and you will unite with the Sniper and the Sapper.
Moving on from here is quite easy. Knock out or kill the technicians on the way, and plunder all boxes you find (use 'F7' often; there are total of three apart from the one you found earlier). At some point, pick up a soldier's uniform and keep it in your inventory (it will be useful later). Soon you will see a ladder going down. Go down with the Green Beret. There will be two guys here. Take them out whichever way you wish. For example:
Bring all your men over to the next room, where the Spy will join you.
We will surface now. You can explore the rest of the underground, but it's of no use. There are no goodies to take. No point in wasting time.
After the cut scenes are over, transfer the uniform you collected earlier to the Spy (if you don't have one, go back and pick up one now). Get the Spy to wear it and then "look-climb" the ladder right next to where he is standing (i.e., press "Z" to turn on "Examine" mode and then climb).
You should see a lot of guys walk by (if you took an unduly long time to surface, then the enemies would already have left, and you won't see what I am talking about). Once two motorbikes (with side-cars) have gone by, it's safe for your Spy to surface (tip: whilst you are "examining" a door, window or ladder, left-click to enter, or right-click to cancel).
Now begins a series of "distract and kill" operations. The technique is quite straightforward: Use the Spy to distract the target. Approach him from a proper angle (because you don't have the ability to order him to look/go elsewhere, yet). If the victim is the sort that patrols, wait at a suitable spot along his path and then distract him. Then, sneak up on him (from behind or the side) using the Green Beret and knife him (if you are more humane than me, you can knock him out and tie him up). Also note that there's no need to take pains to hide bodies unless I tell you so explicitly. For the most part, you can just kill and move on.
Refer to the screenshots. Distract Guy #1. Get the Green Beret to climb the ladder and come out (make sure Guy #2 is not watching nearby). Take out Guy #1. Then, distract Guy #2. While he stays distracted, kill Guy #3. Stash his body (in the place marked by the red "X"). Kill Guy #2 and stash his body as well. Come back and grab Guy #1's body and stash him away as well. Now get the Spy to go inside the nearby building (door marked with a yellow circle). NOTE: There's a goodie crate near "X", but you can ignore it. You don't really need the molotov cocktails inside it (on the other hand, it's so nearby and tempting...).
Inside the building, in the first set of rooms, you'll find two soldiers and an officer. Take out the soldiers using t