Competition and Search Frequency
Quickly, competition is the number of websites that are in the Google index for whatever search term you are working with. Search frequency is the number of times whatever search term you are working with was searched for in Overture over the past 30 days. Actually, it isn't necessarily Google or Overture, but the software that you'll use will be returning results from those engines.

Keyword Extrapolation
Keyword extrapolation is nothing difficult. It really refers to running your keywords through some software that provides you with previous searches that contain your keyword. So if you input "widgets" an extrapolation program will provide you with all the keywords searched for with widgets as part of the search term. You'll get results like blue widgets, red widgets, yellow widgets, widget pizza, etc., etc. You will often get an exhaustive list back that you will need to go through, phrase by phrase, to decide which are relevant to your market, and which are not. You will nearly always get a lot of terms that just don't fit into your scheme.

The reason behind extrapolation is to turn up search terms that you hadn't thought of yourself. I will tell you from experience that sometimes you do and sometimes you don't. Having worked with clients who already had established websites and had already done a great deal of keyword research, I found that more often than not the original keywords were right on target. However, if you are starting up a site, or haven't done any keyword research in the past, it is certainly worth looking into extrapolation. It's amazing what some people search for.

Wordtracker.com is a great place to keep an eye out for keywords. They keep a running tally of the most often searched for keywords and publish both a short-term and a long-term list of them. This is a good way to see where search terms are seasonal, or are responsive to news stories and events. If you are looking to break into a niche market this is a good place to start as you will be able to see what terms are searched for on a regular basis. Their publichsed list shows the top 200 searches, both long and short term.

Choosing Keywords
I shouldn't have to tell you that you want the keywords most related to what you are selling, publishing or whatever.

Don't ever, not on your wildest dream, try to attract people to your site with keywords or phrases that have nothing to do with your business. It used to be that people would use the top searched for phrases on their site, and in their keywords meta tags, to attract traffic to their site. Users would arrive looking for something that wasn't there, and promptly leave, a bit ticked off. Eventually the engines realized this and added a fix for this dilemma to their algorithm.

When you run your search frequency and competition levels is when you will really select your keywords. Initially you'll want to go for the keywords with the highest search frequency and the lowest competition levels. These will pay off well, and they'll also be the easiest to optimize for. Your exact, most relevant keywords will probably have high competition levels, and probably high search frequency as well. You will definitely want to go for these, but realize that it will take longer to get listed for them. Start off with the easier keywords and phrases, keeping your eye on the best of your keywords and over time work at getting listed for them.