It starts with following what you want. I played 2fort pubs for almost 400 hours before thinking "Highlander would be fun with the people on my server. I want to play engineer."
That team fell through, so since I still wanted to get into competitive, I formed a team with friends for 6v6, and decided to learn medic. This was around the time of i46 with Classic Mixup, so I got to watch PYYYOUR and Shade a lot (mostly PYYYOUR).
Whatever class you want to play, look up some of the best players in that class. The My Gaming Edge series covers a lot of basics for things like 6v6, but I'm not familiar with anything for Highlander.
But Highlander is the easy part, almost any class at any lower levels aside from Demo doesn't need any set guidelines. You can try your own stuff. Find a team in UGC Iron/Steel (http://www.ugcleague.com/forum/forumdisplay.php?61-Highlander-Players-Looking-for-Teams), and that can be your start in the competitive world. From there, just go wherever your newly developed skills take you.
Until then, TF2Center is the only real option for playing with competitive players.
Also clorg's directions are pretty accurate.