The things you will need:
filled out application
application fee
proof of competency
Here is the state police website with permit
info.
If you are former military you can use your dd214 as proof of competency otherwise follow the state police link's for list of competency.
The application will be submitted to your jurisdictions circuit court clerk, I suggest you look at there website and if you have any questions they normally are more then happy to help and answer questions.
The application fee will vary jurisdiction to jurisdiction. A few years ago the requirement for fingerprints went away and a lot of jurisdictions dropped the application fee because of that. My jurisdiction went from $50(the max that can be charged) to $15. The permit is good for 5 years and must be carried with a photo ID, no one leaves home without there drivers license so that is never a problem.