Since Twitter changed its API its become more complicated to put a Twiiter feed onto your WordPress website. You now have to apply for a token which sounds a lot more hassle than it actually is.
Here is 6 simple steps to get your Twiiter feed to display in a sidebar or footer widget
1. In your WordPress dashboard go to Plugins > Add New and install Simple Twitter Tweets (or one of the many other Twitter widgets).
2. Go to https://dev.twitter.com/apps/new and log in with your Twitter account details.
3. Fill in the form by adding your username, web address and description (I just added web designer for this) and click the Create your Twitter Application button.
4. Scroll down to the bottom of the next page and click the Create my access token button.
5. Click the OAuth Tool Tab and you will get the 4 keys you need to add.
6. In your WordPress dashboard go to Appearance > Widgets > Simple Twitter Tweets and add your Twitter name and the four keys from the OAuth Tool tab.