Here's the U.S. Forest Service Manual on axes, which explains how to do this properly in detail:
https://www.fhwa.dot.gov/environment/recreational_trails/publications/fs_publications/99232823/
Basically, you want to leave the handle around 1/4" or 3/8" proud of the pick. It should be a tight-ish but not super tight fit before you put the wedge in (basically, you want a good close fit all around the handle). Rasps and cabinet scrapers are your friend here. Also, when you pound in the wedge, hit it evenly across the top with a non-metal mallet to reduce the chance of splitting it (or put a wooden block on top of it and pound on the block).
Some people add metal wedges at a 45° angle to the wooden wedge, but this is more controversial. A wooden wedge done right needs no metal wedges, and if there's no metal, it's easy enough to drill and remove the wooden wedge and slide the head back off the handle at a later date if you want to adjust things or add a thicker wooden wedge when the handle dries/shrinks.
Linseed oil is your friend with wooden handles -- it swells the grain and makes the head tighter on the handle once it's installed (never use water to do this, as it works temporarily and then leaves you actually worse off when it evaporates in a couple days).