First, do not panic and do not pull on the tether. Both of those will likely make the situation worse.
Try to assess the situation:
- Where had your come from?
- What direction is most likely to release you from your position?
- Can you move the ROV at all?
- Does the rear camera help determine the problem?
Next, go ahead and try to pilot your way out. If the ROV is mobile, but your tether is stuck, fly along the tether to see if you can retrace your steps and untangle. If you have a manipulator, that can help to grab the tether and move it around and hopefully sort out the tangle.
If you really are stuck, you might have to disconnect the sub from the control box and seek divers or another ROV to assist. If safe and appropriate (not creating a hazard to navigation), tie a float to the end of the tether so your sub is easier to find when you return with help. Worst case you might need to cut the tether. Be sure to have a good GPS position or set of bearings so you can find the location again.
In some cases, you might be able to maneuver the ROV to the surface, turn off the power and disconnect the ROV and pull the tether back through the entanglement.
It is also good idea to train for this situation. You can do that in a pool (where recovery is assured) with a PVC frame or even a pool deck chair. Try to tangle the ROV/tether in the worst possible way and then untangle it.