Mark center lines on mat, and floor of car to aid centering. If needed; trim with small nibbles at a time while trial fitting around floor shifter and console if equipped using center lines to keep consistent repositioning.
Once fitted to shifter etc., transmission & drive shaft hump, fit to door openings if needed.
Yes, heat gun used sparingly will ease wrinkles and puckers from mat; also letting mat warm in sun will be productive. Door sills, and kick panels will hold outer edges of mat once it is correctly relaxed & positioned. Limited use of spray contact cement is a good idea to secure top edge of mat along fire wall. Work slowly with patients one section at a time and the job will come out nicely.