I have the same question! My arthritis is worst in my knees and feet, and troublesome in my hips and getting worse in my fingers.
I look at all the squats and step aerobics some people do - OUCH! It hurts to get on the floor and then up again, so I avoid Pilates and yoga and situps and such things. My dr. suggests swimming, but there is no gym with a pool nearby and I am not at the point where I can leave my family that long every day.
However, this is what I DO do. It's been three weeks this time, but I have done these things for several months at a time on and off through the past years.
1. Walk. I take a slow pace and then speed up as I feel able...but I do not go so fast or pound the pavement (I walk on city sidewalks) so hard that it hurts. Slow and steady may not lose me as much weight as hard and fast, but I can walk daily and do 1-2 miles at a time without it hurting. This adds up!
2. Strength training. Well, sometimes I joke that it is weak training, but it is better than nothing! 3x per week in the morning I do seated and standing exercises for my upper and lower body. I usually watch a tv show while I do it, as I get way way bored with exercise videos. My routine right now (I just graduated myself to 3lb weights!) alternates upper and lower body exercises. I chose them from different websites, like Spark People, Youtube and Livestrong. Leg lifts, seated rotations, overhead presses, etc. I do 15x reps of each exercise and just go through the list and repeat till the show I am watching is done - 25-30m or so. Again, it is not very much compared to some who have no joint pain or who are stronger, but it is so much better for me than just sitting around.
As for the pain...I will take Aleve when it is bad, but I never push myself so hard that it hurts more than I can bear. And I allow myself to rest afterwards when I need to.
Hope that helped you some!