By far the easiest and fastest method is to use the free Twitter username search tool. Just go to the tool, Enter in the username, press the Search button. In about 3 seconds you will get a clickable list of every single person who is a member of Twitter that matches that username.
If you know the persons full and exact Twitter username then performing the search will display a thumbnail of that persons profile and information and will be the only one that appears in the search results. Simple click the thumbnail and you will be taken to their full profile page with their information, tweets, etc.
As long as you know part of the persons username then you can still search for them by username and find them. The only difference is the search results will display thumbnails of all profiles that partially match the username information you entered. Scroll through the search results until you find the username you are looking for, click on their thumbnail and you will be taken to their full profile.
Real simple. In any webbrowser simple enter the following url in the browser address bar:
Replace the part [username] with the actual username you are searching for. So for example, lets say you are searching for the username evan. The url you would enter into the address bar of the web browser would be ...
Here is an image of what you will see:
