SOLO/MP ESCAPES:

CHOPPER ESCAPE
The easiest way to escape is with a blue and red key. You could aquire one for each escapist.
Leave during the free time before final roll call. You can find the warden's chopper on the roof above his office.

Alternatively for a group escape you can use a make shift ladder and a screwdriver for the vents outside his office. Then use a maxed out clippers and each hold a blue key to get the the roof.
You can also get to the warden's chopper from the guard's quarters west of the office.

WORKING MAN
There is a job available with a prime spot for powering off the generator and discreetly picking and cutting your way out. You can access the generator room through the vent with the aid of a makeshift ladder. You could also tunnel your way out from the gen room.
(If you have escaped using this tactic please upload a screenshot for me and your ranking)

SQUAD CAR
This escape is available but not recommended because it would require a lot of crafting. To get into the garage you will have to simultaneously turn off 1 of 2 generator, so you can cut the fence.
(If you have escaped using this tactic please upload a screenshot for me and your ranking)

TIPS:

You will need to take your contraband back and forth through the yard using the purple doors because of the detectors. These purple doors become one-way at lights out.

Knocking people out around the cell block takes the longest amount of time for the medic to respond.