There are several ways to use Twitter from a Nokia mobile phone, and here at the E71 blog we have brought you a couple of ways; some free ones and others paid ones.
Gravity is no doubt, the coolest and best Twitter client out there for Nokia phones. Unfortunately, is is not free! The other option is Dabr.co.uk, but it is not quite and application, is just a website.
So that leaves place for the perfect Twitter client, TweetS60. It is free, unlike Gravity, and it is a client unlike Dabr. I have been using TweetS60 because it is free of course, and does its job pretty well. You can check out TweetS60 at the Ovi Store: TweetS60

i like twibble better …
i use and like very much. Snaptu.
Free.
Yes, in my opinion twibble is better too. TweetS60 was VERY, VERY slow on my E71, and was very unresponsive and unstable.
I use it. They just need to add an option to vibrate/ring when a new tweet is posted.
I use Gravity on my 5800XM while twibble on my E71. twibble gets updated frequently and got more functions and ease of use lately, having alert function is a must have IMO. I also like Dabr on Opera mini (e.g. twitpic thumbnail) I can jump to tweeted URL and back to twitter quickly. TweetS60 is a good twitter app to start with.
I second subcorpus’s comment – twibble is free and does a remarkable job…