The Freehand & Region Tool now has a Magnetic Lasso mode which allows you to easily trace around objects in a photo to cut them out. Turn on Magnetic Lasso using the toggle button on the infobar .
To start tracing around the edge of an object in your photo, click on the edge. Then click again a short distance further along, to trace the edge between the two click points. Continue clicking around the edge to trace around the object.
If at any point the line misses the edge you wanted to follow, hit Backspace or Undo to undo the last click point. Then zoom in and click closer to the last point, on the edge you want the trace to follow. You will need to move in smaller steps along any parts of the edge that are less clearly defined, but where the edge is clear against the background you can move along the edge in much bigger steps.
The example image shows 6 clicks that are highlighted to cut out the shape within the cup's handle. Objects with a more contrasting background works best, and whilst this image could be done in even less clicks, more nodes generally produce a more accurate outline.
When you get back close to where you started, click on the start point again to complete a closed outline.
Once you have a complete closed outline, switch to the Selector Tool. You can now copy (Ctrl+C), cut (Ctrl+X) or delete the selected part of the photo.
Once you have cut out an object, you can usually improve the edges by applying a small amount of feathering using the feather control on the top bar.
You can also use the eraser tool to remove other areas that are not needed.
From version 12.1: