Piece of cake.

The first thing you need to do is use a good liquid (spray) stainless steel cleaner/protectant about once a month. Wipe the stainless down with a damp cloth first to remove any grunge. When dry, wipe down with the cleaner using a soft cotton cloth. Once this is applied, all the prints will be gone and it will leave a protective coating that will resist further prints and marks.

The best cleaners to use are the commercial S.S. liquid spray cleaners from Zep or 3M. You should be able to find one or the other at Home Depot, or a variety of other home/hardware stores.

You only need to use the cleaner about once a month. For daily cleaning between applications to remove marks and fingerprints, simply wipe the stainless down with a slightly damp microfiber cloth, and all marks will come off and it will look like new again without needing to use any cleaner. The cleaner will leave a thin protective coating on the stainless (just like waxing your car), allowing marks to be easily wiped off.

What you are looking for is
Zep Stainless Cleaner (my personal favorite) or
3M Stainless Cleaner.