The best way to care for your cast iron furniture is to use a soft cloth or sponge and a warm soapy water with liquid soap or even a cleaner like 409 if there is grease on them. If you are using an ornate table base with lots of nooks and crannies, you can also use a scrubbing brush. Be sure to not use an abrasive cleaner as the cast iron is coated in paint or powder coated and if you rub through that, you can get down to bare metal and cause rust to form. It is also suggested to not use a power washer on them as that can cause the paint or powder coating to peel off.
The best way to protect your cast iron restaurant furniture is to wax them once in a while. It is best to use a spray on wax as it would be difficult to apply with a cloth or sponge with all the nooks and crannies in them. Be sure to test your chosen wax on a small unobtrusive area to test that it does not discolor the finish.
If you do find rust, you will want to use a fine sandpaper or wire brush to clean the area, I would then apply a rust converter just to be sure you got it all. Once you have done that, you can find a paint that will match the finish and touch up where you did the rust removal. I would be sure to test the paint in an unobtrusive area to be sure that it will match or at least be a close match to the current finish. Once you have re-painted it, be sure to put some wax over that as well.