Mine doesn't have a surround either. This week, doing some preventative maintenance and winterizing, I notice a wet spot under the tub. My shower walls are a linoleum like on the floors. The seal around the tub was a trim piece with butyl tape where it screws to the wall to keep water from dripping between the tub and wall. I removed the trim pieces and siliconed the area around the tub. I used a whole tube of silicone and got it between the wall the tub really well. Then I got new butyl tape and reinstalled the trim.
With respect to cleaning, just wipe it down and periodically check under the tub for any leaks.