I have white-rodgers 1F82-51 programmable A/C thermostat. I would like to replace it with a regular thermostat, which one should I use and what is the wiring procedure?

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Below is your original owner's manual and wiring diagrams.

http://www.white-rodgers.com/wrdhom/pdfs/instruction_sheets/0037-5650A.pdf

There are many available thermostats to choose from so I suggest you shop around for the best deal you can find for a 2 stage heat 1 stage cool heat pump thermostat.

You need a heat pump thermostat according to the thermostat you have now since the model number you provided is for a heat pump thermostat. 2 stage heat and 1 stage cool. I mentioned this two times so you do not make a mistake and get the wrong thermostat.

Identify and mark if necessary all wiring attached to the present thermostat and there attachment points/terminal designations then attach new thermostat using the identity of the wires just removed from the old thermostat following the new thermostats wiring diagram. IE R to Red,W to White,Y to Yellow ETC.
Make sure to read the entire manual that comes with the new thermostat since you may have to program it for your system. Last but not least if you do not feel comfortable doing the thermostat change over by all means call a professional since we cannot be of much further assistance since we are not there to see exactly what you are working on. Good luck.