Any link to your site can help build link popularity, so the number of ways to build link popularity is nearly beyond count. I'm only going to focus on the most common methods here, but if you can think of a new and innovative way to get people to link to you then by all means go for it. More methods will be discussed in detail in a further article on link building methodologies.
The most obvious way to get people to link to you is to ask them, however this method is often overlooked or purposely ignored by people who simply believe that it won't work. Simply asking people in fact works very well, you just need to do it right.
The first thing you need to do is locate your targets, who is it that you want to link to you? Well if you want to rank #1 then the people that link to the #1 site need to link to you right? To find out who links to the #1 site search on Google for your desired keywords and then using the toolbar check the backward links of the first site that comes up. These are the sites that you need to get to link to you. Now it may not be possible to get all of them, but get as many as you can.
Why would someone add a link you might wonder? Well if your site is well designed with plenty of useful content (and if it isn't then you need to go back and read the rest of this site where it is explained that quality matters), then why wouldn't someone want to link to you? Part of the value of a website is that it can lead you to the right information if you can't find it there. So having a list of links to high quality content rich sites adds value to the site with the links. You'd be surprised at how many people will add a link if you ask them nicely. It also doesn't hurt to mention how you think your site would be a good resource for their visitors. This is especially true with amateur sites, and believe it or not amateur sites are important. Sure these sites might not have the best designs but since they've been online for years they've accrued quite a few inbound links and a high link popularity rating. The people who run these sites aren't out to make money so they don't mind linking to you if you have a good site, they're noncombatants so to speak.
If you can't get a free link you might be able to get a link exchange, where you link to their site and they link to yours. This is more typical of for-profit sites. Here is where the Google Toolbar will again come in useful. You will be able to tell which pages have a higher PageRank so you know which ones will be worth it more to exchange links with. I don't want to suggest that every link doesn't count, because they do all count. Sometimes though you want to limit the number of links you have and this is one way to do that.
When sending out these link requests you need to be careful about spam. Contrary to popular belief spam is any unsolicited email. The message doesn't have to be commercial, it doesn't have to be bulk. Sending a single unsolicited message can be considered spam and if the recipient complains it may be enough for your host to suspend your account. So if there isn't an email address available on the site for comments, suggestions, proposals, or anything of that nature then you shouldn't just blindly email them. Some people really hate solicitations and it is better to be safe than sorry.