Like many of the above - 1/8" and under - I just replace. Anything over that gets sharpened by hand on the bench grinder. Freshman year of High School, we had a great metalshop teacher - very old school, but memorable. One of our first projects was to make a drill bit sharpening gauge out of 1/8 steel plate. Cut the shape with a hack saw and file all the edges to a line. The graduations were scribed-in by hand. You had to be able to correctly sharpen a drill bit before you would be allowed to use the drill press. He looked over our shoulder to be certain that you could get two nice continuous chips off of your sharpened drill bit. If not, you didn't pass "GO".
Similar with the lathe - everyone had to make the good ol' tool post wrench (with scriber in the handle) to be able to use the lathe - AND you had to successfully sharpen the tool bit as well. We also learned to forge a cold chisel from hex stock, heat-treat it as well as a center punch and sand cast something out of Aluminum (I don't recall what I cast - that was over a half-century ago).
We then had to demonstrate proficiency at using both the vertical and horizontal mills as well as the surface grinders - making a C-clamp - the screw you turned on the lathe. I laugh at that now because at work we have over 40 journeymen machinists and I think only ONE of them even knows how to chase threads, but he uses a CNC lathe, so that's cheating...
We had to make a small hammer - and that was turned - complete with crisp knurling. Drill and tap the head - chase threads for the handle on the lathe.
We also had to do some rudimentary sheetmetal work - torch soldering with a an acetylene torch, then brazing followed by oxy-acetylene welding. Only then did we try our hand at stick welding.
Our teacher was a real maestro - the shop had only 6 small South bend lathes and he rotated everyone around the shop to the different stations to complete the list of tasks. If you got everything on the list completed, he would challenge you with fun stuff - like welding aluminum with a torch. THAT was ugly, but it is possible.
I must say, the lessons learned in that class, as well as all of the other shop classes I took really stuck with me and I still use the skills today. It's a damn shame that most of the High Schools have discontinued them, but I don't make the rules...