“How do you relieve pain after tooth extraction?”

Hopefully, your practitioner would give you appropriate instructions, but if they don't, you should ask them - all practitioners have their own preferences because some use NSAID's (Ibuprofen, Naproxen [Aleve]) for their anti-inflammatory effects and pain relief, and some still hold onto older, less desirable tendencies to prescribe narcotic pain relievers, which led to the opioid crisis. We always recommended naproxen (Aleve) or ibuprofen (Motrin) to patients as long as they weren't allergic to NSAID's (or they were contra-indicated by their physician due to other conditions such as history of gastric ulcers, bleeding disorders, etc.

Don't rinse for 24 hours after the extraction.Take 600 mg of ibuprofen and alternate that with 1000 mg of tylenol every four hours.

The pain is coming from the disruption of the tissue in this area. The best way to reduce pain is to take an over the counter pain med or a prescription medication.
Most pain resolves significantly in a few days iT should be only a few days

Your Dr. should have told you. Take advil or aleve with food as directed unless your physician told you not to.

Best method is pain and anti-inflammatory medications. Sometimes ice can help if there is any swelling. You should obtain detailed instructions from the practitioner that performed the extraction procedure.
Good luck.