Daily Routine
Spend the first couple of days in jail just checking the place out. Stay out of trouble and make a note of the daily routine and then stick to it.
Useful Items
While you are learning the daily routine keep an eye out for items that could be used to help your escape. Items like duct tape, wires, files, and cutlery which can be used to chip away at walls, the ground, or fences.
Plotting Escape
Once you have figured out the daily routine take advantage of the times you are left alone to plot your escape.
Inmate's Desks
Searching other inmate's cells is a primary source for finding items, its worth doing daily as the contents of each desk can differ from day to day.
Mailman Job
Consider doing the mailman job when it is available as it allows you to enter inmate's cells and search their desks without attracting guard heat.
Guard Uniform
Stealing a guards uniform and wearing it is a good way to wander around and explore the prison grounds outside.
Craft Pouch
Craft a pouch as soon as you are able to using foil and duct tape so you can secrete contraband items such as screwdrivers. If you don't have a pouch contraband items will be detected and confiscated and you will end up in solitary.
Create Stash Area
Dig an alcove or unscrew a vent in your cell to create a hiding place for your secret items.
Intellect
Avoid the temptation of just boosting your strength and speed, the stat that requires a lot of attention is Intellect. The higher your intellect, the more jobs and items you are able to craft become available to you.