Welcome!
Looking for a game, you'll have to be sure you choose one using the right edition of D&D. Don't worry about being a rules-master, just read the basic stuff and ask questions when necessary, learn the rest at your own pace.
PbP often runs slow, I think an average of one DM-update per week might be the case, but some games run faster or slower than that (some require multiple updates per week, for example).
If you don't have any D&D books at all, it's probably easiest to just look for a 3.5 D&D campaign, since most of the core rules are available in the online System Reference Document (
a link here to the Hypertext d20 SRD, since the official one on
WotC's website is clunky and slow to download/navigate). If you have a 3.5 D&D Player's Handbook, then that works too. 3.5 games are still common here.
If you have a
3e D&D Player's Handbook, that also works, but not many people run 3.0 games around here anymore, besides me (well, planning to anyway). If you have a
4e D&D Player's Handbook, that's the newest edition and it works too. Each has some differences (kinda minor between 3.0/3.5, major for
4e). Given your newness I would assume you aren't starting with the older OD&D, BD&D, or AD&D.....
You can also look to similar games like Pathfinder (PFRPG), which is just a revised version of 3.5 D&D, sort of, and the Beta version of the PF core rulebook is currently available for free download as a PDF (or multiple PDFs, one per chapter) at the
Paizo website. This is only a recent arrival, though, and there aren't a lot of games being run for it yet. It would probably be best to use the 3.5
SRD instead for a start, since there are more 3.5 games running/starting at present.
Finding a game shouldn't be too hard, but just be aware that many Play-By-Post games die off quietly at random times, as one or more players and/or the DM quits or just gets too busy with other stuff and forgets about the
PbP. Don't be discouraged if a game just stops updating for a long time and dies off. There are plenty that DO last months or years, just not as many as the ones that get interrupted by this strange thing some wierdos have that they refer to as "life", or just by flakey people dropping a game for no apparent reason.