Search Tests
Jira has a very powerful issue search facility and since a test is an issue-type, all the different mechanisms that you can use to search for issues, apply to tests too. On selecting the Search Tests menu option, you are taken to Jira's Issue Navigator with the "Test" issue-type pre-selected thereby allowing you to search for tests.
Please refer to Jira documentation for different ways to search.
Search test executions
If you are looking to search through the executed and unexecuted tests that are part of a test cycle, then the Execution Navigator will allow you to do that. This is accessed by picking the Search Test Executions from the main Tests menu dropdown.
Please refer to the Search Test Executions section for more details on how to do this.