Scraping off the old and putting new ones on ! How the hell else are you gonna do it ?
I don't really know how but it's important to do it before Christmas! :)
Take off old .. Repair surface if needed ... Replace with new .. Easy peasy
Check your local regulations. You may be required to put a water proof, but breathable material (like tarpaper) down before you put new shingles on. Even if there is no regulation about the waterproof material, it is smart to put it on anyway. Then put new shingles on (I am assuming you take the old shingles off first and check out and repair roof)