Consider just taking the window to a local hardware store and let them replace the glass. They tend to be reasonable and since they do so many windows, they tend to be fast and cheap on the labor and do excellent work.
Wear protective gloves and remove the broken glass. Put it in a cardboard box or sturdy garbage bag. When all the glass is out of the frame, tape the box/bag up for disposal and mark it clearly “Broken Glass. " Place the box/bag wherever your trash pickup might be. Use a wet cloth to pick up any small shards, and toss the cloth out with the rest of the glass.
Optional step: carefully brush linseed oil on the surfaces that will be holding the caulk. This extends the life of your caulk job, but it takes a day or more to dry, so plan your time accordingly. It is a very good idea to prime the wood with exterior primer or use exterior varnish to seal the wood. This will make the wood last decades. Without sealing the wood, it might rot in only a few years.
Measure at both top and bottom to see if the window is plumb. If the shape of the window isn’t square or rectangular, make a paper template. There is a very narrow shelf-type area that the glass lays on; there may also be one side, usually the top, slotted to receive the glass. Remember, you’re measuring where the glass lays, not the visual opening.
1/8th of an inch can cause the upper piece of wood to sag over time. Using 1/16th of an inch smaller makes fit tighter and is better for supporting the wood. If you use glass the same size as the opening, it will stretch the wood and might make the window harder to fit (or leave small gaps at the corners where water will get in and rot the wood).
With the frame secured to a flat surface and the bottom of the window closest to you, hold the glass at a slight angle top to bottom. Guide the whole pane slowly on the “shelves” and work toward the top. When you’re just about there, carefully lay the glass almost flat, then guide it as you slide it into the groove at the top of the window. You may need to use one hand on top of the glass, the other on the bottom.
Open the compound can and put a lump about half the size of a tennis ball (use more when you get the hang of it) into your left hand (right if you’re left handed). Work it until it’s soft and warm. You may have to replenish the supply in your hand more than once, depending on the size of the window.
