1981 Basic, page B61:
PLAYER ADVANCEMENT: If no one has reached the 2nd level of experience in three or four adventures, the DM should consider giving more treasure. If most of the players have reached the 3rd level of experience in this time, the DM should consider cutting down the amount of treasure, or increasing the “toughness” of the monsters.
I have spent a lot of time thinking about character advancement rate over the years, and I’ve tried various methods to control it and make it fit my outlook. None of these attempts have been particularly successful.
Personally, I have long tended to think that about 3-4 sessions at first level and another 3-4 sessions at second level are “about right,” at least for mid-XP scales like fighters. If playing a regular weekly game this would mean a month or so at each of the first two levels. However, since I seem to have trouble gaming with any real consistency, the rate ends up feeling agonizingly slow and the fragility of low-level characters means that even surviving four straight sessions can be quite a challenge. Character deaths slow advancement even more, as players need to start over at zero.
At one point, I even gave up on traditional XP for a while, using a Roll to Advance system. While that system got characters advancing at the rate I wanted, it (by design) removed any connection between success and advancement, pegging increases simply on the number of sessions played. While this was what I was after at the time and it seemed to work well enough, at some point I tired of it and returned to traditional XP.
I use XP for treasure recovered and monsters defeated, usually shooting for around an 80/20 split. I am a big believer in gold as the measuring tape for success, and I rarely give XP for role play, class skills, or anything else.
Personally, with our less-than-frequent play, I’d be fine with slightly quicker advancement at early levels. It seems that I am rarely running games where the characters are in the “sweet spot” of 5th to 8th level. For quite a while years ago, I actually awarded 3 (or sometimes even 5) experience points per gold piece recovered to speed advancement while not turning PCs into millionaires.
At the end of the day, though, I think the best way to speed character advancement is to simply play more often. (And don’t play elves…)