Let’s say you’re targeting keywords with a high competion and with an extremely high spam density. Something like “Buy cheap viagra online”. The top 10 in Google is filled with a couple of .edu’s, a .gov and a few other domains. Looks really competitive to me.
Now go out and build some Google trust. A public job at Google would be extremely suitable to let your website gain enough trust. If you’re website is trustworthy, go add “Buy cheap viagra online” about 7 times to a 9,000 words page. Make sure that the page attracts a few hundred links.
Now get someone to add a link to your webpage with the anchor text “Buy cheap viagra online”. That link doesn’t even have to be an authority link by the way, a single link from a website like this should be enough.

Oh wait, a link from this website is enough. Did you spot the “Buy cheap viagra online” link in the blogroll of this website? It’s filed under “sponsored links”. It has been there for about a week and a half, Google has cached it 4 days ago. A website that wasn’t present in the top 1000 for “Buy cheap viagra online”, is now ranking 3rd for the targeted keyword. Hey, that’s our friend Matt!

This means that it’s quite easy to get some good rankings in Google, even when you’re targeting competitive terms. All you need is three things:

1) Trust
A somewhat older website (> 2 years) with lots of links (> 10k, with at least a few hundred of high quality) is a solid foundation for good rankings. This is a really important factor, if not the most important one.

2) Keywords
Ofcourse, your website needs to mention the keyword’s your targeting. On a page with around 8,000 words, a keyword density of 0,1% should be enough.

3) A link
If you succesfully implemented 1) and 2), a single link with the right anchor text can be a trigger for Google to rank your website.

Edit: I just noticed that Matt doesn’t even need the “online”, he ranks #5 for “Buy cheap viagra“.