I did not drink any coffee today, so I will try to answer this question to the best of my ability. Go to Google and type in the keyword you want to check for competition. Now comes the tough part, click enter. For more precise results, go to Google and type in your keyword wrapped in quotes. Still the difficult part of hitting enter is required. Seriously, this is a good way to see how many pages are listed for a keyword. Now that you had your coffee, I'm sure it clicks.
Look at the top 10 results, that's who you are really competing against not the other 20 Million pages of rubbish who happens to mention the word.
Use a keyword suggestion tool to research alternative keywords and the long tails. The top ten sites are only part of your competition.
Actually I know a really useful search engine to see what PPC keywords your competition is using. Here it is: keywordspy(dot)com
That has nothing to do with the original question, and besides using a keyword suggestion tool is "the worst" way to to compile data for long-tail keywords.
Many times companies will target the long tail version of keywords and build out adding services or company to the keyword as in web design services or web design company. Just because you don't see them in the top ten results doesn't mean that they are not breathing down your neck.
find the results for your keyword and the people that are above you or near the rank of your site are your competition.