Treat your first 3 or 4 prisons as complete learning experiences
Use the planning tool before you start building.
After planning your buildings, run the utilities before starting the build, as that saves time.
A power generator can have 16 capacitors around it to add power - after that you need a separate generator on its own circuit and the circuits/capacitors must not touch, as they short out
If your generator goes off and you can't get it back on, check the capacitors, as they each have to be on before you switch the generator on.
Pause the game and flag all incoming prisoners for a search - I've had drills, bats, even guns found on new inmates!
Fences are free (not outer walls - they're expensive) - make sure you have a secure compound before your first prisoners arrive, else they will keep trying to leg it.
I've always gone for an 'airlock' style entrance, using fencing - that way, you can assign a guard to the room between the gates and he will open the doors for workers/visitors etc.
Funding - you start with $10,000 but if you click report (bottom right) then Grants, you can grab another $80,000 - a much more reasonable starting budget.
Solitary cells don't need to be 3x2... I use a single square with no furniture.. that'll learn 'em
Forgot the most important one... it's an Alpha and crashes frequently (I find it gets worse the bigger your prison is) so save, a lot!