tinyurl.com is providing service for shortening any long url.
The short url will be useful to remember it and also it will be useful when we are having limited space for specifying the url.
For example, twitter will allow only 140 characters. To save space Twitter is using tinyurl service.
Even we can manfully create the tiny url to use it in twitter to effectively handle the 140 characters limit. ie First shortern the long url using tinyurl.com and then enter this tinyurl with your message in twitter.
We need to use tinyurl only when it is really necessary or useful.
Because, it is having its own drawbacks. The reliability of tinyurl is still in question. Because, if the tinyurl site goes down for few minutes we can not access the url for those few minutes even when the actual website is not down.
tinryurl is functioning based on 301 redirect which will not affect the search engine ranking of the site. Anyway, I am not sure whether the search engines will consider the tinyurls exactly same as true urls.
You can enter your long url here to get short url using tinyurl.com
Some bookmarklets such as twitlet/ are available to make this easy. i-e just we can enter the message and url in a pop-up window of bookmarklet and then it will be automatically send to twitter after shortening the url.
This main difference between the use of tinyurl in twitter and twitlet is, twitter will restrict the 140 character limit even before shortening the url. But twitlet will truncate the message based on 140 characters limit only after shortening the url.
bigtweet.com/ is also providing similar bookmarklet. It seems it is having more features. But comparatively it is loading slow. For more details you can read
10 awesome Twitter tricks.