How much training does it take to be a decent bicycle mechanic?
It depends on what you consider 'decent' really... The sad truth is that the majority of shop mechanics are pretty mediocre. A really good mechanic will have literally decades of experience and some things, like wheel building, are more art that science and some mechanics never get good at it. Like anything else, you learn from doing it... over and over and over again. I've built wheels before but, to be honest, they're garbage because I just haven't built enough of them to come close to mastering it. There's a difference between being able to do something and doing the right way if you know what I mean.
It also depends on what kind of mech you want to be... A mechanic at the local family oriented BMX shop vs the local "Performance Bikes" mech vs a high-end road or mountain shop's mechanic are very different things. It's like anything else, the mechanics that work at a high-end automotive tuning spot are a far cry from the local Ford dealer's mechs... Likewise, the guys working on $15,000 road bikes and $10,000 mountain bikes are at a whole different level than the local bike shop's mechanic. If you want to be an average local shop mech, you can do it with a handful of years experience if you're at all mechanically inclined.. If you want to be a truly "good" mechanic, you'll be learning 10 years from now. If you want to just do basic work on your bikes... just get a decent tool kit and have at it but be prepared to make some mistakes and wind up at your local shop feeling like a dummy, lol.
Like Bob said, it's pretty simple to do... but like anything else, being excellent is a different ballgame and will take patience.
Also, whomever said most people that race know bikes up and down.. I'm afriad you couldn't be more wrong. They know what they like, what they don't like, and will notice even the smallest changes but most of them would actually struggle to build a bike from the ground up compared to your average mechanic.