2005 Ford f 150 AC blowing hot air compressor not coming on. What should I cheek first.

Not blowing air or cold air? No cold air need to check the charge. All doors need to be checked to make sure they move fully. A partially opening or closing door will feel hot on a hot day. I think you need a new car guy and you need an ac guy.

It is low on coolent,

Is the compressor running when it blows hot air ?

No there is not really a thermostat. The first thing you need to check is to see if the AC compressor on the engine is engaging, if not you likely have a refrigerant leak and need that repaired and the system evacuated and recharged. Always confirm the problem with i have laid out with a professional HVAC tech before starting any repairs.

The most common cause for an AC blowing hot air is the system is low on refrigerant. A small leak will eventually lose refrigerant until the compressor eventually will shut down. Most compressors require a minimum of 20psi to engage and chill the air. Most certified service stations can diagnose and recharge most systems for $100-150 depending on where the leak is. There are do it yourself kits available at most auto parts stores that come complete with leak detector (R-134A with dye to show where leaks are) compressor oil, and a recharge hose.

Need a little more info. Does the blower motor still blow? Have you checked the fuses? Is the ac compressor engaging?

Should be at the bottom of the engine, between the engine and radiator.

Selection lever does not move to AC vent or floor vent only to the defrost. AC compressor does not kick in when AC is selected.
Vacuum level is at 18 instead of 23.
Any suggestions.

The A/C system has a pressure switch will keep the A/C from running if the freon is low. It prevents damage to the A/C compressor from low freon.
My bet is you'll need to recharge the A/C system.

Check both high pressure and low pressure switches if a/c still won't come on check resistance at the clutch your a/c clutch is bad and will have to be replaced.