Get to the elevator
After the cut-scene is finished walk toward Ort-Meyer's corpse and take his car keys, then make your way through the basement until you discover the elevator. Finding the elevator is trivial. On the way, you may pick up syringes from a room with a patient inside. You will also see many 48 clones lying dead on the floor everywhere; those are the clones you killed in the last mission of Codename 47. If you have the Ort-Meyer key card, you can also obtain a minigun by using the syringe on a patient and a Gold Desert Eagle dual lying on the floor, both in places with a keycard reader outside the door. They are cool, but cannot be used outside the level (? verify this) and aren't useful for a Silent Assassin run. Warning: The minigun will seriously slow you down and running won't help.
Obtain a disguise
Go to the second floor via elevator. There are lots of dead patients lying around. Take the clothes of any one. (On Normal, you can pick up the SWAT disguise and SPAS 12 and walk out of the front door, but this will not work on higher difficulties. There you need to be a bit more subtle, as described next.) You may pick up all the melee weapons on the ground, but don't forget to holster them. You need at least the syringe or the stun gun if you don't have any syringes left.
Get the SWAT disguise
Now follow the doors with green exit signs till you reach a staircase going three ways. Take the left or right stairs down, and go through the left door (left when you are facing the SWAT members). Now wait for a single SWAT member to come down the spiral staircase. Let him start moving up, and follow him. If he sees you, get down till he has his back to you, then again move up. Anyways, when he goes through the last double doors, wait outside with a syringe/stun gun in hand and sneak mode. Look through the keyhole and when you see him going towards the glass door, open the door and move towards him. Sedate / tase him from behind and take his clothes.
Now go through the glass door and climb down the ladder. Wait till the SWAT guy at the car is on the other side of the car. Now rush to the door and quickly escape in the car. You will get Silent Assassin and the CZ2000 Dual.