I've run several successful PBPs and several unsuccessful ones. (It's been a very long time since I did PBEM.) This is based on my own experiences only.

Have good infrastructure

I usually set up a phpBB-based forum solely for use with the PBP, rather than using an area of someone else's forum. It makes it much easier for me to administer and tweak.

I set up custom ranks for each player to indicate which character he or she is playing, which makes it easier for the players and myself to keep things straight. I encourage avatar use as well.

Another advantage of having your own forum is that you can easily set up "private" forums, each of which only a given player can see. This is useful for "note passing," keeping track of xp and private conversations, and so on without having to go through a backlog of PMs.

I usually have an out-of-character forum for intros, general discussion, and metagame stuff, and an in-character forum for actual play. I devote a separate thread to each "delve," as I'm currently running an OD&D campaign.

Be active, have active players, and communicate interruptions

The paramount concern in PBP, in my experience, is having active players. I ask for some kind of substantive post at least once a day. Stagnation is doom in the PBP realm — once things slow down, heat death follows. If I can't post for a few days — which happens — I let everyone know, and expect the same.

Start the game with clear direction

One thing I discovered running a City State of the Invincible Overlord PBP a couple years back is that too many options at the beginning of play can lead to decision paralysis as the players try to decide what to do. In a dungeon-type game, I'd recommended starting at the adventure site, getting stuck in, then getting to the roleplaying after the players have the swing of things. In a story-type game, I'd consider starting in media res, like with a chase scene or something that gets the players thinking in-character quickly.

Pace your background exposition

Finally, I'd avoid excessive infodump. It's great for you, as the referee, to know lots about your setting, but I'd keep the early background to just enough to give the players a sense of things and parcel the rest out through play.

A single PBP doesn't need all that many players, so "advertising" may not be the best approach. First consider all the techniques already listed on this site at Where can I find other RPG players? Even if the game is online, it might be nice to have friends, acquaintances, or even just people from your area in it. Here's an example of someone using meetup.com to advertise for a Demon: The Fallen PBP in the Denver area. This has the additional benefit of maybe turning into real tabletop at some point.

Also consider whether you really need to host your own PBP. There are a lot of PBP sites (and forums) out there already, like rpgcrossing.com and rpgm.com, and so PBPs on them are somewhat more self-advertising. Most are free and are simply forum-driven.

Speaking of forums - forums are still the #1 kind of site used by gamers. As a result pretty much every large RPG forum - rpg.net, enworld.org, etc. have places to advertise for games both in person and pbp, and often just run pbp there on the forums as well. Most every RPG publisher has a forum as well, and most will have dedicated subforums to these as well or at least be friendly to them in a general announcements subforum.

RPOL.net is for online forum gaming, but they do have an Offsite Gaming forum where they allow posts for other PBPs.