How can someone who is old, overweight, and suffering from arthriris lose weight?

Live better. There is no age at which one cannot exercise & eat better. Improve your diet with lean proteins, fruits/veggies, & only 2-3grains/day, drink alot of water, decrease 500cal/day to lose 1lb/week. For exercise, do pool exercises since the heat helps & is not hard on the joints, or a reclining bike or walking on soft surfaces can help. Yes its harder but you can do it.
Walking program. Start with a walking program at your own place. Start very slow. Walk for just few minutes, take break and then walk again. Slowly you'll build up exercise capacity to walk longer distance without getting tired. Control calories in diet as well to get the most out the weight management program. Please note, weight loss will improve arthritis pain as well.
Important. Make sure your meds do not promote weight gain. As some pain meds might.