Social bookmarking is a good place to start. If your site is new, build them slowly.

Low competition keywords are really the ones that are just over 1000 searches per month - always take into account serch volume as well as low comp words.

Be clear on your keyword category
Do your research on the SUCCESSFUL sites that are using your keyord - what are they doing that makes them so great?
Do an in anchor search to see website linking back to the anchor text - links have been built elsewhere on the net and you need to find out who your competition is!
Do an intitle search
Remember that this kind of thing doesn't happen overnight - Google will often trust older domains than newer ones (sorry!)...

Hope this helps a little!

Elle

Why do you want low competition keywords ? there's a reason that they are low competition, they don't genereate much traffic because they are not searched a lot

Check your Analytics to find long tail keywords you're being found for, then do some SEO to improve your positioning for those - Web 2.0's, contextual links, social bookmarks, etc.

Also check out Keyword Sniper Pro from Jack Duncan to find more related keywords that the GAKT might not show you.