How to rank someone else's website number 1

It is in my best interest to rank someone else's website number 1 for a search term.

I did a keyword revealer search, and found out the keyword I'd like to rank number 1 for has a difficulty of 22, which is really low.

This person is my friend and the search term is the name of their company, without the quotes.

Their site ranks number 1 in both Yahoo! and Bing! for this keyword, but around 16 on Google.

This is a very small SEO project, but I would like some advice. I would like to help this guy out.

For ranking a website, it is very important to look for some of the Google search key factors such as: keyword density, title of your website, links, and use of social networks.
And to correct others site, the first and foremost thing is checking their onsite as well as correcting it. After the correction of on-page or after optimizing an on-page the another important factor that you have to do is link building activities.
As, you know that SEO is a combination of On-page as well as Off-page. So, it is very important for a site to make it a proper balance of these two methods.

Apart from SEO, another important factor is SMO. Through these you can also make aware peoples about your site, as social media is one of the best way of informing people as well as search engine about your site.

The keyword is: "Company Name"
The domain is: "companyname.com"
The title of the domain is: "Company Name"

Did I get it right?

We can't answer any question if we don't know what you have done.

What did you do on linkbuilding? On-site SEO?

If we know this we can give you tips on your strategy. You need to know what's broke in order to fix it

From your post, this seems to be really easy to do. Just building 5 to 10 quality backlinks, you should see your rankings improve.

Also, don't forget to focus on onsite seo.