They do proper SEO the same way I do. Their SEOs are not noobs wasting time on forums looking for the next push-button free & easy method.
When you have cashflow and you have a budget, even a modest one, you can build lots of good links. If you know how to approach them and what to offer ANYBODY will "sell" you links. You don't have to pay money for them, you just have to give them something so it is win-win. For example you could find sites in your niche that look like crap and offer to redesign them. This might seem as a lot of work, but if you are or you have a very good web developer you can redesign a site in 2-3 days and ask for a lot (e.g. 100 links from within posts to 50 of your sites in your massive site network). There are shitloads of "out of the box" methods and they are all 1000 times better than comment spam, forum spam and what most noobs use. That's why I always say ANALYZE THE MOST SUCCESSFUL SITES!
Regarding buying links, it works great but they cost monthly so personally I don't do it that much. However there are sites who do SEO exclusively through link buying. For example huge businesses like Panasonic for example buy links. I'm not saying that Panasonic buys links for sure, I am saying companies of that caliber do. I had blogs with PR2-3 and I got contacted by SEO companies offering to pay me $10/mo for a link on a PR2 page (highly relevant to the site they were working for). I negotiated for $20/mo for the link with upfront payment for 6 months (they played hard but accepted finally and I knew they would because I knew they had huge budget). Then after like 3 months contacted me and said their client stopped using their services and asked me to remove the link after the 6 months pass, then when time was due I got an email reminder again. This is gold for us because they pay a lot for a link and that link is to a high quality site so you might have gave it away for free

. That blog of mine was a support satellite and excluding the $20/mo from that link + another $10/mo from another link it was making no revenue. So these 2 links were covering for domain & hosting and bringing in a tiny profit each year.
Aside from buying links, those that are really good build site networks like someone said here. For example the conclusion I reached after serious analysis is that manysites (including my competitors in a given niche) have bought hundreds of EMDs (exact match domains) and put blogs with 10-30 pages on them with videos of their reviews and 100 word original text + 100 word copied text from their review pages, with links to their review pages. So they made sure nobody outranks them because they own an EMD - they bought them - and also push link juice to their site not to mention the link exchange leverage that a large satellite network gives you. Even so, they were behind me for many keywords because I was doing a better job
Also do not neglect viral and high quality content. On an established site with existing massive traffic, quality content can increase links and traffic naturally. Some of my high quality white hat sites were doubling the number of links and traffic every year. With a viral campaign (even a shitty one) you can get to PR2 in a couple of days (the PR won't be visible in the Google toolbar but will exist as real-time PR/link juice). I made a site with funny stuff because I was getting emails with fun things from friends so thought to post them on a site since I get them. So I was posting and one day I got a funny "Windows Vista source code" image. So I posted it on my blog and voted it on StumbleUpon adding it with the title "Vindows Vista source code stolen by Russian hackers". In 5 hours I was getting about 500 visits/hour and traffic held to 10,000 visits/day for a week then slowly dropped. After that I did another vote on StumbleUpon for another post, that bought traffic as well. After 2 weeks I had like 500 natural links from various blogs, including from PR4 homepages. This resulted in my site getting a PR2 after a couple of months when the toolbar PR got updated.
There are countless ways to build links. So many that you just don't have time to do them all. Happily most "competitors" are noobs and just use XRumer and ScrapeBox and half of their day they spend it on forums looking for the next "secret method".
If I'd have to give ONE piece of advice to a friend starting SEO, it would be this:
NEVER EVER FOLLOW THE PACK!