How to fix door trim?

Hi... I have a '93 Cavalier. The door trim is coming off, and I need advices on how to best remove it completely to clean the adhesive off of the door, and what to use to stick it back on to make it stay.

I tried some double-sided thick tape, but it didn't stay. I don't know if I'm explaining this properly...

Some would say take it off, makes the car look cleaner...but if you want it on, and all else fails, then just use some clear RTV silicone (can be bought at Autozone for like $3)

Thanks... is there a product out there that I could use that would easily remove the old adhesive?

Mother's Clay Bar...its a bit pricey (I think $20-30) but it will take off just about anything short of wax and clear coat :)

Ooor, you can do what I do, and rub it off with your thumb (beware I had a blister on my thumb the size of a quarter for 3 weeks afterwards!)

Before you decide to put it back on, though....here is a pic of my car after I took off all the molding and badges...

http://img398.imageshack.us/img398/1008/10000511dx.jpg

Before putting back the trims I suggest painting them with a special vinyl paint for trims and bumper very good product and glue them 8 inch by 8 inch with a hot glue gun good luck