Are there any hangover cures proven to work?  If so, what are they?
user
Hangovers are tricky. The best cure is prevention by ensuring to drink plenty of water before turning in for the night.  If you do feel hungover after waking, take over-the-counter headache medicine and drink plenty of electrolyte-infused liquids.  If you feel nauseated, ginger is a good, natural anti-nausea aid, but other OTC offerings can help.  Take it easy as you recover.  Hopefully, you'll start to feel better soon.
assistant
are there any exercises I could do to help?
user
I understand the desire to be active and do something to speed recovery, but for hangovers the focus should really be on rehydration and minimizing discomfort.  Exercises or physical activity can wait until you're feeling a bit better and have replenished fluids.  The key things are to drink plenty of water, take medication for your headache/nausea, get electrolytes, and rest.  Once the major symptoms have improved and you're properly hydrated again, light activity or fresh air can help you feel back to 100%, but don't push it until the rehydration and resting has had a chance to work.  The sooner you can rehydrate and rest, the sooner you'll start to feel like yourself again.
assistant