First things first, you'll need a good mattress protector as added insurance against spills, stains, and dreaded dust mites, even if your mattress's cover is removable or washable. Most offer easy care instructions, and the best designs should not disrupt any special cooling features your mattress may have or even be noticeable.
When you do need to clean your mattress, and from time to time you will, even with a protector you'll want to spot clean any visible stains or odors and leave plenty of time for it to air dry. A good vacuuming with an upholstery attachment is also beneficial for pulling out inevitably embedded dust mites, dead skin, and other allergens.
For the longevity of your mattress, it may be useful to flip the mattress but follow the manufacturer's guidelines.