Click in the search bar. It doesn't matter whether you're in a project or not for searches.

Within the basic search bar, Asana has several pre-made saved searches for you such as: 
1) Tasks I've created
2) Tasks I've assigned to others
3) Recently completed tasks

If the pre-made saved searches are not specific enough, click "Advanced search"

Advanced search allows you to search by assignee, within a specific project or group of projects, specific collaborators, attachments, completion status, and due dates. These are the basic level of advanced search. These can be used in any combination.

In addition to what is available on the main screen for advanced search, you can also add additional filters to be more specific. For example, "Completion date"

app.asana.com

This guide provides step-by-step instructions on how to effectively search, use advanced search, and save searches in Asana. It covers both basic and advanced search options, allowing users to search by various criteria such as assignee, project, collaborators, attachments, completion status, and due dates. It also explains how to share and save search results for future reference.