Right, I have a few keywords I want to target for my website.
How do I go about targeting these keywords? Where do I start?

Do I just put backlinks with the keyword on high PR websites?
I've updated my content?

How can I get into google with the keyword?

Thanks in advance.

submit your link to social bookmarking and your articles with main keywords to article directories.
Posting in 4rums have high PR with URL's signature also important to get PR

For achieving your targeted keyword set it in some way that little same as query entered by people. Use many techniques of SEO like blogs , directory submission and articles. But from next time first observe about people's demand and according to that choose your keyword.

First you need to do On Page SEO. Then link build.

Social Bookmarking
Forum Posting
Link Wheel
Blog Commenting
Article Submission

Social Bookmarking, Forum Submission, Profile Linking, Blog Commenting, Link Exchange is useful for you. Try it.

1.Forum Posting
2.Blog Commenting

Both are best way to get up your keywords on google results.

Googleblogs.com ---> Research "keywords" Then find the blogs, post your comments there.

There are mostly Do-Follow.