Monofilament fishing string (can break), braided fishing string, wire fishing leader, windshield removal kit (Harbor Freight or the like), PVC pipe cable saw (home depot or lowes), or a long thin knife like a filet knife or razor knife.
The knife option is self explanitory in that you will make a couple passes but you have to be very careful not to knick the paint or molding. I think I would pass on this option as it would be just my luck.
Wire cutting option. The monofilament and braided line is probably going to be your most forgiving but will take the most time. The wire fishing leader will be more aggressive so caution will be needed. the windshield removal kit and the pvc pipe cable saw are going to be very aggressive so they will be fast but again lots of caution not to damage paint and trim.
Once you have the trim off then you will need to wash the area where the trim was and then dry it. The fastest and best way to remove any remaining foam tape is with a 3M stripe off wheel that you can get from Amazon, paint supply houses, and most auto parts stores. It is not cheap but when properly used will not damage the paint.
Amazon product ASIN B00063VT0G
Once you have the tape removed then wipe down with denatured alcohol and have a beer or beverage of your choice. At this point you are read to prep the moldings which means getting all the tape off of them and then wiping that surface down with denatured alcohol. Now you will need 3M adhesive promoter and 3M tape to reinstall.
Amazon product ASIN B000P18N76
Amazon product ASIN B00B3I1JR6
Prep the moldings by applying the adhesive promoter where the tape will be installed then install the tape. Next prep the paint on the car where the tape will attach and then install the moldings.
LMR has a couple of videos how to align, remove the tape and install the molding so watch these videos in order: