one of my first was a receiver for a specific tv remote to run a duct taped robot, rip the 40khz ir reciever(i bought 10$ tsop.. nice smooth digital output much easier), and tie it to a pin, i used a pic 16 or 18 i think, first write code for a read loop (hint, read delay times between on an off, but have a large buffer waiting, in my remote the strings were several bytes for the device code and several bytes for the command, after good reads , start reading other buttons and you will be able to resolve the hex commands.
from there, compress and save...
spitting back out is almost just LED on a pin, but you need to vibrate the 40k carrier, aswell as the I/O time, i ended up using a flasher circuit tuned at 40k and powered the flasher from pic output
But the first thing to check is the carrier frequency of the remote you are trying to get in to