The process is outlined in full on the Stack Exchange Q&A forum, but in short, it involves downloading a program that will allow players to edit the contents of an iPad app - in this case, FTL: Faster Than Light - then locating and copying the prof.sav file from your extant PC or Mac version of the game. Since the recent FTL: Advanced Edition expansion creates its own profile on PC and Mac, those who have the addition installed will also need to copy the ae_prof.sav file to their iPad to ensure the game unlocks that content as well.
Honestly, it sounds more difficult than it actually is, and anyone with a basic understanding of how to move files from one folder to another shouldn't have too much trouble. We attempted this file swap trick moments ago, and it worked like a charm after less than 10 minutes of effort. That said, make sure you create backup copies of all files before you move them, just in case something goes horribly wrong.