The way I do it is:
1: Wear latex gloves like the doc wears for those oh so plesant prostate checks.
2: Put adhesive on both the weatherstrip and the door where the weatherstrip will go using the finger of your choice. Dispose of gloves.
3: When both sides are tack free start sticking the weatherstrip to the door. It works like contact cement. You can wear a clean pair of gloves but it isn't normally necessary.
No mess, no muss, no fuss.
