Make sure you do <verbatim>NameOfYourWidget</verbatim>. If you didn't, nothing will show up. So if your page is MediaWiki:TwitterWidget, make sure you do <verbatim>TwitterWidget</verbatim>.
If you did that and still nothing works, make sure you are putting it in the right place. If you are putting it on the main page, try putting the verbatim tag at the top of the page after your previous save, then preview, if it works, the you are done but if you made a mistake however if it didn't, go to your MediaWiki page and check if the code is correct.