If your screen isn't lined up with the outside on the PCB silkscreen, you may want to adjust it so it's properly lined up with the cutout in the enclosure.
Carefully slide a razor blade or small putty knife underneath the display and use the edge to push the adhesive off the foam tape.
Be cautious and avoid scraping the silkscreen on the PCB (as that could cut a trace). This may remove some of the stickness of the foam tape. Carefully peel it off.
Place and Stick
Add a new piece of foam tape to the same spot on the display. Line up the display with the outline and press it down to stick it into place.
Add GPIO socket header
Insert the header into the GPIO on the display. Use a mounting putty on both sides of the header. Press it down to temporarily secure the header in place.
A Panavise Jr will help hold the PCB in place while you solder. Place the PiTFT PCB into the Panavise Jr. with the header facing out.
Position the PCB so it's in a comfortable orientation for your hands to solder (lefty or righty?). Heat up your soldering iron, and grab some solder. Apply solder to the pins.
Check that all the pins are soldered nicely and there's no bridging, cold solder, shorts, or unsoldered pins.