The symptom of broken shifter innards is a loose shifter lever, which wobbles but won’t change gear.
First, check that the shifter cable hasn’t broken off very close to (or inside) the shifter. If it has, make a mental note to find out what the cable is rubbing on at that point, then follow directions for a broken gear cable – use the stick method to hold your derailleur in place, as it is very unlikely that you will have sufficient cable attached to the bead left in the shifter.
If the cable is fine, then most likely the shifter innards are shot. The insides of shifters are full of springs and ratchet mechanisms. If this doesn’t scare you, first attempt to fix the mechanism, or at least jam it in one gear by getting the ratchet to engage. This will mean opening up the shifter – a job which is typically easier on more expensive models. Of course, the price of failure is also higher on more expensive models.
If opening the shifter is not an option, or this fails to work, it may be possible to hold the lever in one position to maintain a sensible gear. Use zip ties, wooden wedges, etc., on the lever to keep the correct tension on the gear cable.
If this fails, follow directions for a broken gear cable.