I do not know all of the specifics of the law, but at a bare minimum you will have to have the seller ship the handgun from Indiana to an FFL dealer in IL. You would then go to that dealer to complete a form 4473, go through the NICS check and pay that dealer whatever their transfer charge is. You would obviously also have to follow whatever laws IL has in place for purchasing a handgun.
You absolutely cannot complete a face to face transaction, in Indiana, and drive back to IL with your new handgun, unless you like federal prison. Likewise a dealer in Indiana cannot hand you the gun to take home. They MUST ship it to an IL dealer.
I see BE Mike is faster than I am. He got his post in while I was typing mine.
IN law states that dealers can ship to IN residents and residents of adjacent states, however IL law does not allow IL resident to accept firearm directly from out-of-state dealer. Just use your local FFL dealer. He will probably only charge you $20-$25 depending on whether he wants your future business or not.