@Anywhere is a Javascript-heavy solution that involves you registering an application and transparently using a primitive form of OAuth 2 to negotiate a user’s relationship with your website. It includes some friendly widgets and if you’re adventurous, some interesting possibilities with Javascript.
Web Intents, the Tweet Button, and the Follow Button are all alternatives to this approach that offer more frictionless experiences for end-users – there are no applications to authorize, no API keys for the developer to work with, and the features work both with or without Javascript. These all use the user’s existing session on Twitter.com to perform actions, without creating any relationship between your site and the user.
If you’re wanting a stronger, API-based implementation, I recommend using sever-to-server REST instead of @Anywhere. If you’re wanting to keep things simple, I recommend using Web Intents.