Links to a site are also called backlinks. There are many ways of getting backlinks - directory submission, blog commenting, forum posting, article submission etc.
thats right. if you have a link on some other site, then you are getting a link back from that site to yours which is a backlink
Yep thats pretty much what back linking is. However, a contextual link text with your keyword in the link is more valuable than lets say a http://www.google.com link.
I might be missing the point, but for the purposes of SEO getting backlinks is so you can index and then rank highly on Google and other SE's.
so lets say i post on someones site "Check out site.com" would that be best? Btw, is site.com or www . site.com better?
Are you talking about in a blog comment or guestbook? I wouldn't. It's spamming. You can often put your site in a URL field along with your name and email address, save the comment space for actually giving a response, feedback or opinion that is related to the blog post. I wouldn't even mention 'visit my site by clicking through on my name'. If your response is intelligent and thought provoking, people will. It gets real old real quick to have to see feedback after feedback with people saying 'visit my page' or 'click on my link'.