How do I see what stories I need to move forward to the next sprint at Azure DevOps?

1. Go into "Backlogs" under "Boards" and click the filter icon at the upper right to unlock the filter controls. At the filter controls change "Assigned to" to yourself and yourself only, and change "Iteration" to the sprint you are leaving. If these two items are not in the filter, click "Column Options" above the filter controls to get them there.
2. Go into "Queries" under "Boards" and click "All" at the upper left. Click "Assigned to me" and then the "Iteration Path" column to sort by that detail.