Spread drop cloths over a large table or work bench. Take the glass door off its hinges using a screw gun. If the door is a sliding glass door, pull it off the tracks. Lay the glass door on the drop cloths.
Unpack the pet door from its packaging. Pull the two halves of the pet door apart. Set one side of the door onto the glass in the position you want it to be installed, keeping in mind the height of your pet. Trace the outline using a marker to create a cutting template to follow.
Put on gloves. Wet the glass with a spray bottle, then use a glass cutter to score the cutting template just drawn. Do this several times on one side until a discernible gouge appears in the glass.
Turn the glass door over and score the other side, following the transparent cutting template and gouge. Score several times to cut through the glass. You may have to turn the glass door over more than once and repeatedly score it until the glass pops out under gentle pressure.
Stand the glass door upright on the floor, having a second person hold it steady. Take one half of the pet door and insert it into the hole. Hold that piece in place and insert the other half of the pet door on the other side.
Insert the retaining screws into the pre-drilled holes in the four corners of the pet door and tighten with a screw gun to clamp the two halves together, setting the door securely in the glass.
Reinstall the glass door onto its hinges or track and clean with glass cleaner, wiping it with a cloth.