Zotero provides several types of support if you run into questions or problems.
Use Zotero's Documentation Help when you have questions about the Zotero workflow, for example - how to save articles to your library, how to change citation styles in a Word document, or how much storage space you get for free. Expect to find simple screenshots and text that walk you through how to use that element of Zotero.
Use Zotero's Forums for help when you have questions about problems specific to your computer, problems with a specific database, or suggestions for improvements to Zotero. For example you might search for why Google Scholar isn't adding articles to your Zotero library, or why Word for Mac 2008 isn't cooperating with Zotero. Expect to see questions other people have posted to the forum and the responses to those questions.Sometimes you will need to look through several posts to find a solution that matches your need. It can also be better to search with a few broad keywords to find more solutions.
If you want to post a question or make a suggestion, you will need to log into the forums with your Zotero login name. Responses to posts are typically posted within a few hours. You should receive an email in the emailbox associated with your Zotero account when a response is posted.