Remove the bolt.
Push the cross pin out that acts as a firing pin stop.
Remove the firing pin and the spring/plate underneath.
Clean everything very well, including the channel the parts run in.
Before putting it back together, clean and inspect the face of the bolt and the extractor.
Does the extractor still have a hook on it?
( It sounds simplistic, but Ruger's extractors are prone to breakage and often the gun will continue to run with a broken extractor as long as it's clean. My Mark II has a broken extractor and it will run a couple hundred rounds before it starts to jam.)
If it's broken, or if you can't slip a spent case up under it and have it hold it firm against the boltface, replace it.
Now clean and inspect the breechface. You may have to use an old toothbrush slathered in solvent for this. Work the breechface over very well.
Also flood the little recess the extractor goes into right next to the breechface with solvent. Let it stand for a short while, then use a toothpick to make sure there isn't any hard crud inside.
Next use a .22cal bronze brush, and from the back end, cover it with solvent and rotate it very well inside of the chamber.
Be sure to use a .22 cal brush. Don't use, as is often mistakenly recommended an oversized brush. If the brush is oversized, the bristles will lay down flat and not work. It's the tips of the bristles that do the cutting, not the sides. (As you can tell, this is a pet peeve of mine.)
If you have a spent case from a Stinger or Yellowjacket, it helps to shove it into the chamber first to scrape the walls clean. You may or may not opt to run the brush down the barrel at this point. I always run a brush down the bore of my .22's. Some do, some don't. My .22/45 has had hundreds of instances of a brush going down it's bore, with no ill effects. YYMV.
@ this point, use a Teflon based grease - Tetra is excellent - and apply a light coat to all the surfaces of the bolt, inside and out, and let it sit.
Next turn you attention to the magazine(s). Disassemble them and use a solvent coated bronze brush to scrub out the insides. Work the brush hard, and use a lot of solvent. Pay particular attention to the inside front where the nose of the bullets ride. I guarantee you that if you haven't taken the mags down and scrubbed the inside, there's a witch's brew of crap in there. Owing to the location of the magazines inside the gun, it will be full of unburned/half-burned/burned-on crap. Clean the spring and the follower also. Follow it all by drying all the parts well.
@ this point, use the Tetra grease and cover the inside of the magazine with a light coat, and also the spring and follower, and let them sit.
Now clean inside the frame. I use a lot of solvent and an old toothbrush and the good old flood it method, then shake it out, followed by blotting up the whole mess with a dry rag. The only real areas I take any care of doing a detail are where the trigger parts work against each other, and the side where the trigger disconnect runs against the frame. Those, I brush, blot dry, and apply a drop of oil (I use Rem Oil - you can use what you prefer).
@ this point, go back to the bolt and all the parts. Use a dry cloth and remove the Tetra grease. Don't buff it in an attempt to get it all off. Just firmly rub it off. Apply a single drop of Rem Oil to all the mating surfaces and reassemble the spring/plate and firing pin and push the retaining pin back in place.
@ this point, go back to the magazine(s) and wipe off all of the Tetra. Again, rub firm, but don't try to buff it all off. The surfaces should feel smooth, but not slick. If they feel slick, there's too much grease. Reassemble everything, but don't use any additional lube on anything except the spring. I usually put a small amount of grease on the spring and wipe it off. 9 times out of 10, the 2nd application of grease will leech out some additional dirt and crud from the spring, no matter how well I've cleaned it.(or though I have).
I know it seems long and involved. It really isn't. I usually takes between 5 and 10 min extra over a simple field strip to detail strip the bolt and magazine. After doing it this way a few hundred times, it's become automatic and takes me probably 20 min from start to finish. <- way less time than it took to type or read