What adhesive do I use to mount a glass pane in shed?
In the olden days (read: until a few decades ago), most windows were built and repaired with glazing putty. It's basically rolled in the palms until warm and in a rope, then pressed against the glass-frame joint with a putty knife or other flat tool. You'd use a smaller bead between the back of the glass and the frame, too, as a seal.
The outcome is ideally something like this, which seals against airflow and sheds water:

More on that
Nowadays (inasmuch as we re-glaze anything in the first place), you can use glazing tape. It's quicker, less messy, and maybe more suitable for beginners. If you use glazing tape you may still want to run a bead of silicone around the outside to lock things together more robustly.