So long as we're talking about 3-speeds, I encourage folks not to be intimidated and do the job per factory rather than sling seeping oil all over their rear wheel. Maybe that's just me. Anyway, SRAM (Fichtel&Sachs) and Shimano 3-speeds come apart with a cone wrench and std. open-end wrenches. Sturmey & Sturmey copy 3-speeds can be tapped apart with a drift punch. There are lots of manuals, guides and videos on this.
OP here. I am contemplating the hub overhaul, though it's intimidating. The subject bike is my daughter's and now she is saying it sometimes slips out of gear (not sure of which gears) and in the highest gear, while pedaling, there is a regular clicking noise (similar to sound it makes when coasting, but I haven't listened to it myself.) It's a Shimano 3cc 3-speed hub with a coaster brake. Did all 3cc hubs come with an integrated coaster brake and would diasassembly of the brake be part of the hub overhaul? Just wanted to know what I'm getting myself into.