The UTM system is a rectangular coordinate system. Since zones are less than 1000 kilometers wide there is no point which is actually given the coordinate 0,0, and all UTM coordinates are positive.
Zones are also divided into sections designated by a letter.
Inter-zone distances are more difficult than that, though. A little bit of information about using UTM coordinates and USGS topo maps is contained in one of the handouts for our land navigation training . UTM coordinates are printed on those maps if you know what to look for. A crude Java applet which implements these formulas appears below. One of the crude aspects is that there is no button to choose West longitude or South lattitude.