Twitter offers a page to help you construct your Tweet Button:
On this page, you have the option of how your button will appear:
The text that people will include from this Tweet can be customized
The URL that you want linked to this Tweet
The default language
You can also recommend up to 2 people to follow for this Tweet button to recommend to the visitor
When you have completed the customization, it's easy to insert the code into your site because Twitter will generate it for you. Cutting and pasting the code into your site will complete the process and then you are up and running.
That's it. It's a very similar process to the Facebook Like button.