This is Singer Featherweight Stitch Formation 101! If your Singer Featherweight is skipping stitches, not stitching at all or perhaps looping or causing an awful thread mess on the underside of your fabric, then this video tutorial will show you the easy tips for what you can do to fix it and save you a trip to the service technician.
Skipped stitches and bobbin thread that won't pick up are most commonly caused by the needle incorrectly inserted or the machine threaded improperly. If you changed your needle lately (or even if you haven't), then you might need to check to make sure it is inserted properly into the shaft. The flat side of the needle faces left on a Featherweight. If it faces towards the back (like most modern machines) or towards the right, then the top thread will not pick up the bobbin thread properly. This prevents a stitch from forming.
The other issue could be that the thread is going through the needle from the wrong direction - it needs to be threaded from right to left as shown in the photo below.
Here's a video tutorial for proper threading of the machine:
Also, if the machine has had its throat plate removed at all, then you will want to check to make sure that the positioning finger on the bobbin case base is properly positioned. A2 needs to be set in B2 as shown in the illustration below. This can cause a nest of threads on the bottom fabric or cause the thread to keep snapping.