This is one of those jobs that looks simple until you're doing it. The first mistake people make is using the wrong mortar, hard Portland-heavy mixes in older brick work can actually damage the brick over time because the mortar becomes harder than the brick and stress transfers to the units instead of the joint. For pre-1930s brick, use a softer lime-based mix but match the profile of the original joint as closely as you can... if it was a weathered joint, don't finish it as a tooled joint. Also clean out at least 3/4 inch deep before you pack anything incand dampen the joint before applying so the old brick doesn't suck moisture out of your new mix too fast.
