Where can I get a free domain? Furthermore, how do I get my site submitted on a search engine like Yahoo or Hotbot?
Google is your friend.
All your questions can be answered by inputting succint, to-the-point search terms.
Submitting your website is one thing - getting it to the top of the list is another.
Once your site is ready, you edit Meta Tags into the HTML code. A string of descriptive keywords that match what the searcher is looking for.
Right-click on some published web pages, and choose "view source."
For example, from BluesNews:
meta content="Quake III Arena, Computer, Games, news, Quake II, Sin, Doom, Duke Nukem, Half-Life, Unreal, Jedi Knight, Starsiege Tribes, The Sims, Heretic, First Person Shooters, 3D, Action Gaming, Delta Force, Hardware, Deathmatch, Multiplayer, Information, Counter-Strike, Team Fortress, Carmack, Red Alert, Baldur's Gate"
name="Keywords">
So, if you ran a search using any of the above keywords, the page would come up.