When a tape gets stuck in your VCR, you can always call a repairman to get it out. But if you want to do it yourself, these are the steps a repairman would probably use.
First, unplug the VCR and wait a few minutes. Then re-plug it in and push the "Eject" button. Often, the wait will have reset the micro-controller and the tape will reappear. If this does not work, you will have to reset the VCR.
Use the screwdriver to unscrew the top of the VCR. Try to gently lift it off.
If the top of the VCR doesn't come off easily, look for small plastic tabs that may be keeping it in place. Press those and lift again to remove the top.
Very carefully untangle the unspooled tape from the VCR.
Locate the cassette-loading motor (see figure below) and turn it. Eventually, the cassette should rise up. You can then remove it from the VCR.
If you need to return the tape to the library or video rental store immediately, call them and ask them for an extension. Explain the situation.
Make sure that the cassette does not close on the tape, or the tape may become damaged. Do not exert too much pressure on the VCR parts as you untangle the tape from them. Some of the parts are very delicate.