Jira has a "simple" search interface, which gives you fields that you can select, and an "advanced" search interface, where you can type in a query. When you're searching for issues, at the top of the box on the left, there should be a "Switch to advanced/simple searching" link.
For bugs that you've submitted, you can go to simple searching, expand the "Issue Attributes" section if it isn't already expanded, find the dropdown labelled "Reporter", and select "Current User".
For bugs that you're watching, you need to switch to advanced searching, and use the query: "watcher = currentUser()" (Advanced searching fortunately has auto-completion to help construct the query.)
For bugs that you've voted on, you also need to use advanced searching, and use the query: "voter = currentUser()"