Back in the old days, it would be pretty easy to grab the unique identifier of a Twitter account. These days, Twitter have gotten a bit more tricky and protective of such information.
There are, however, loopholes that will help you grab the unique user ID of a Twitter user and all you need is a browser 😉
For the user that you want to retrieve the twitter ID of, visit this page below:
http://api.twitter.com/users/show/some_twitter_username_here.json
JSON will load in your browser. From there, you should be able to very easily find the id node that contains the Twitter user ID. Enjoy!