You can use many methods to find someone on Twitter, and a good Internet sleuth tries multiple ways. A quick name search on Google finds social links for most people who are active online. If you already know the person's website or blog URL, social links often prominently display on these pages. Another option is Twitter's built-in search function which offers both a basic and an advanced search. Several free third-party search apps exist as well.
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Searching on Twitter
Twitter features a search box on the top right of the screen. Click in the "Search Twitter" box and type in any word, username or hashtag. The results screen provides filters to refine your search. You can save your search for future use using the "Save" link in the middle section. Use the Advanced Search to accommodate several factors or keywords at the same time. You can also exclude words or search for people near your geographical location as well as narrow the search to a date range.
Alternate Search Methods
For search engine like Google or Bing, add the word "Twitter" to the person's name for better results. Search results generally return the Twitter handle and most of the person's bio. Bing results show key statistics like the number of tweets sent and follower count.
Free third-party applications like Tweepz and Followerwonk pair bio photos with Twitter handles in their search results -- which can ease the pain when someone uses a Twitter handle unrelated to his name. Tweepz allows searching on topic, location or skill, and has a free email look-up tool. Followerwonk searches Twitter profiles or bios and includes a "More Options" feature to search Location, URL, Name, follower count ranges and number of tweets sent.