How do I search to see tasks that I completed for a specific day (like today or yesterday)?
You can do to this in 3 different way. You can:
1.) In the Todoist Karma pop-up window, click View All Completed in the Completed History section.
2.) Using the Show Completed Tasks icon in each project
3.) Using keywords: type a keyword in the Todoist search panel to find both current and completed tasks with that particular word.
How do I use filter to see tasks that I completed for a specific day (like today or yesterday)?
That's unfortunately not possible, at least not through searching. But you can click on the Karma score -> View All Completed and here you'll see a full list of all completed task separated by dates. Although this list can't be searched by our search engine, you could use the browser's Ctrl+F option to quickly find the date you're looking for (today's completed tasks will always be at the top).