AddThis provides an official plugin for Movable Type (download). This plugin adds the AddThis button to each post. It is fully customizable.
Don't forget to Register and create an AddThis Profile ID. Customizing your plugin with this ID will allow you to see how your visitors are sharing your content: which services they're using for sharing, which content is shared the most, and more.
Step by step tutorial
To install the Movable Type plugin, first download it from AddThis:
Extract the contents of the archive. Upload the "AddThis" folder to the "plugins" directory of your Movable Type installation.
Sign in to Movable Type. For each blog you wish to use AddThis in, select Design > Templates from the menu.
Add the tag
<mt:AddThis> to the templates that display entries.
(In the MT4 default templates, these are the Entry and Entry Summary templates.)
Republish your blog.
To customize the button, open Tools > Plugins from the top menu. Select the AddThis Plugin and click Settings.
One important customization setting is including your AddThis Profile ID (recommended) for tracking button traffic and usage, button style, colors, and more. If you have not registered for an account, you can do so at any time (it's free!), and select the option to also create a Profile ID for analytics at the end of that process.