Running Your Own RPG
Overview
There are various ways to create RPGs. You don't need to own your own site, although you can if desired.
Message Board Topics - A topic on a message board where all of the things of an RPG are handled, including the actual Rping.
Chat Room/IM RPGs - RPGs are randomly started within Role Playing chat rooms or IMs.
Site Based RPGs - RPGs that are hosted at a site. This includes Message Boards devoted to a single RPG.
Message Board Topic
To create an RPG Topic, find a message board which has a role playing forum/forums set up for player-created RPGs (RPGs where the player who created the RPG is Game Master). Then, read any and all forum rules on creating an RPG. Some forums will require a character sheet to be posted. Also, include a description, a rating (G, PG, PG-13, R, NC-17) that is allowed in that forum, and a bit of Role Play to start things off and get your fellow RPers interested. If you want (if allowed on the board), plug a site describing the world/characters/plot of your RP.
You could create your own message board for RPing, but I’ll go into that in the Site Based RPG section.
Chat Room/IM RPG
To create a Chat Room RPG, all you have to do is create a chat room using IRC, Yahoo, MSN, AIM, or other similar programs. It helps to put 'Role Playing' or similar wording in the title. Alternatively, you can join one, but this is about RP creation.
You will not have the power a normal Game Master has, and these RPGs tend to be less literate, since any 7 year old can enter a chat room. The best thing to do for this style of RPing is to get a group of known good RPers together before starting the chat.
Another way to RP in this style is through instant messages. Get someone to RP with you through IM. Usually there is a setting decided before RPing, and, sometimes, pairings, although it is usually more interesting to make pairings through actual RPing.
Site Based RPG
To do this, you will need a website. While you can get a site for free, it will, normally, not be a top level domain, and may have more restrictions than a paid site. Alternatively, you can use a forum.
The way I recommend this is to describe the RPG in part of the site, and have a forum or embedded chat for the Role Playing. I won't go into HTML here, but unless your hosting service has a site builder or you're using a free forum, you're going to have to know web design.