All you're really doing in the second part of link building is surfing the web. After you've done your competitive links analysis, and compiled the results into an Excel spreadsheet, you should go visit the sites that are linking to your competition.
When you're surfing these sites, there are two key pages you're looking for: the one linking to your competition and the contact page. Finding the first one will let you understand the reason for the link. For example, somebody checking out links to Sitepoint.com would find that they're linked to for being an authoritative source on PHP coding.
Once you've found the two pages, copy paste the url for each into the spreadsheet. You should have 3 columns side-by-side now in the spreadsheet. The first column shows the domains that are linking to the competition, the second column has the reason for the link and/or URL of the page that the competition's link is on, and the third column shows the linking site's contact page.
Personally, I prefer to write down both pieces of data in my second column (the reason and the linking page's URL). That way, I can easily check to see whether a link to my site has been added. I avoid wasting my time returning the site and finding the linking page all over again.
Another little piece of information to look for if you have time is broken links or links to dead sites. This will let you share a tip and make the other webmaster a lot more open to linking to you.