Ok i'm not sure where to put this thread but, I'm deciding to put it here because Web Design and Advertising your website could go hand in hand.

Ok now to the point. Does anyone know of any really cheap way to get very many visitors to your website that you just made?

Another thing. Say I started a web design company. Does anyone know of any way, again, to cheaply advertise it and ensure that many people will visit that website?

Well, this is something that I have done with a graphics website, which is pretty similar to a web design website. (I also have a web-design "company").

What I did is this:

My website is going to feature tutorials, scripts, and all other kinds of webmaster resources, but right now it only has a few tutorials. What I did to attract some attention was submit some of my tutorials to tutorial websites such as www.good-tutorials.com. This bumped my daily visist count from ~15 up to ~1500.

Of course, this isnt as easy to do with a web design site, but you could try and offer some free designs or something, and get them linked to on web template websites.