A photo of the rim would be more helpful, but it looks like rather standard equipment. You'll probably find four bolts going through the middle of the wheel. Removing these will separate the two halves of the wheel rim. Be sure there is no air pressure in the tire when you take it apart because pressure will cause it to pop apart and throw parts at you when you get the last bolt out.
If you're riding on pavement you can wear the tire off until you can see the air inside, and it won't hurt anything. But, if you're riding off-road maybe you'll be more likely to pop a sharp rock through the tire if it's worn off badly. I always like to use things up all the way and get my money's worth, so I wouldn't bother with new tires until the old ones were just about gone if there aren't any sharp flint rocks around.
