Inbound links are what the search engine robots look for; you want sites of related content and high traffic to place a link to your site onto their site, so that you get the benefits of PageRank aka "Link Love."
The fastest way to accomplish this is to write informative (you know, high quality articles) articles that link back to your site, or pages, and have them published on other websites. Inbound links can come from just about anywhere. Whether you have links in your signature of your favorite forum/bulletin board, or you simply link your website on other Social Media properties, these are all links and they're all somewhat valuable. I say somewhat valuable as some links are definitely more valuable than others, and that's all based on overall quality.
The more pages that you have on your site with valuable content, the more inbound links you can have pointing to your site. The exception to this is "Free For All" (FFA) pages which are also called "Link Farms" which can sometimes have the opposite effect and get you banned from Search Engine's. Well, technically speaking. I won't get into "Black hat" or "grey hat" vs. "White hat" SEO, but I'm not going to preach to anyone as I have seen a lot of "less favorable" schemes that work excellent in getting higher rankings in the Search Engines. However, if you are a newbie and you're looking to get longer-term rankings, I highly encourage you to stay away from any linking schemes or "tricks." Also, beware of SEO tools that automate link building. These are not useful for long-term success.
In Google you can find out who is linking to your site by using the three advance search commands:
(Note: Google will only show a small percentage of links that they find, so don't beat yourself up if you see only a few links, or even 0! Tools like SEOMoz's OpenSiteExplorer can help you find out who is linking to you, too)
There are several Link Popularity Checker online; http://www.opensiteexplorer.org/ is one of the best tools there is, although it is limited to non SEOMoz Pro users.
SEO is a combination of 3 major factors:
1. On-page Optimization
2. Off-page Optimization
Now some people may consider links as a part of Off-page optimization, but not me. Off-site Optimization should refer to off-site content that exists on other sites, which will also link to your site. But links themselves should be an entirely separate area.
Each one of these factors are important and together as a unit they can give you good search engine rankings. Be realistic and don't overdo things. Over optimization can absolutely destroy your long-term goals for your site. SEO is not a spring, it's a marathon.