When you have arthritis, you need to make all your regular tasks as easy as possible, and this is especially true in the kitchen. Instead of standing, think about getting a kitchen stool so you can sit while you do dishes or any other jobs where you have to stand for a long time. Another trick is to make sure that everything is easily accessible and easy to move -- no more reaching for heavy dishes or storing pots and pans where they are hard to access. Get lightweight kitchenware and store them where they are easy to get at, perhaps in a self-standing cabinet with a work-surface top. With one of these, you can do all your kitchen tasks at a comfortable height, too.
When it comes to food preparation, get good-quality ergonomic knives that slice through your vegetables and fruit easily. You may even find a pizza wheel can be a useful tool to cut food instead of using a knife that puts a strain on your wrist. Electric tools, like can openers and jar grippers, can make opening cans and jars much simpler; and if you put straps on your fridge or cupboard doors, so you use your whole arm instead of your hand, they will be easier to open too.
Instead of carrying heavy dishes, why not get a wheeled cart to move everything in one go from the stove to the table and back. Another tip is to use non-slip rubber tablemats to hold your plates firmly in place. Large utensils with easy to grip handles and flatware to match will mean you don't have to worry about spillage or gripping problems. Using drinking glasses with holders or holding your cup with both hands will also make things easier; you can also try drinking through a straw if you find lifting a glass or cup too painful.