I've stated on a number of occasions that I can track the amount of traffic that I get to my website through Twitter track tools and these are really easy to set up. In essence these tools offer a service to shorten the links that you put in your Tweets, after all you've only got 140 characters so you don't want to be using these up unnecessarily when you're trying to get your message across.
Use this software to shorten your links and then afterwards you can got back and analyse each shortened link to find out how many people clicked on it. This then gives you important information as to which of your Tweets are giving you the best responses, admittedly it's then up to you to determine whether that is down to the subject matter covered or the quality of the Tweet itself.
The two most common Twitter link shortening tools are:-
Just use the links to click through and sign up for an account. From my experience neither one is better than the other, they both are a similar service and you don't need to sign up for both. Just chose one and go with it.
Note also that if you are going to use a free social media dashboard to manage your account(s) like Tweetdeck or Hootsuite, then these services already have a link shortening service built in that you can either switch on or switch off dependent on whether you want your link text to be visible.