If you go to the Main page, there are a number of built-in views, like "Hotlist", that generally show what you're looking for. You can customize the filters applied for the Hotlist in your Settings. In many cases, this will suffice.
If it doesn't, you can create your own Saved Searches on the Searches page, which is what many of us do most of the time.
For example, you can create a search to find tasks due by today by selecting "New Search" from the list, then adding to the default criteria (|Checked off | No |) another line:
| Due Date | is before | tomorrow |
You can then save the Search by clicking on "Save Search" in the upper right of the list and giving it a name.