Scrape away all traces of adhesive and debris from the Surface's case and screen.

Use high concentration isopropyl alcohol (over 90%) or iFixit adhesive remover and a lint-free cloth to clean the adhesion surfaces on both the case and the screen.

If glue or glass remnants are left behind, the new screen will not mount correctly and may be damaged.

Lay the adhesive strips out to get an idea of where they go.