One of the easiest ways to post tweets to Twitter is to automatically send updates from Facebook to Twitter.

If you would like to set this up, make sure that you:

Have a page on Facebook that is representing the same entity that your Twitter handle is representing (aka a business/club/organization page on Facebook)
Log in to both your Facebook account and your Twitter account (you can do this by using different tabs in your browser)
After you set all that up, you can go to this page on Facebook: http://www.facebook.com/twitter, and select the page from which you want to send posts to twitter by clicking the “Link to Twitter” button that appears next to the appropriate page:

Facebook will then automatically open up a Twitter authorization window where you are basically authorizing your Facebook account to post to Twitter on your behalf.

Once you Authorize app (basically giving Facebook permission to post information to Twitter) then you will be brought right back to a page that looks like this on Facebook to work out a few details about what exactly you want posted from Facebook to Twitter:

After you select the appropriate page in Facebook that you want to link to your Twitter account you will get these options.
You choose the types of activity that you would like to be shared automatically from Facebook to Twitter as you see in the checkboxes above. You could do something like only share specific things you want to promote to a larger audience, perhaps events or photos? It is really up to you and your strategy, I went ahead and left them all checked for McStarter to send to my @McStarter account on Twitter as you can see, this is something I just might change later if I see the need.

I hope this helps! Post any questions that you have below and someone will help you out, have fun posting!!