Your question is VERY BROAD.
In fact imagine all you know about modeling, getting the shape for the character. Now imagine how much such knowledge there is outside your knowledge. In other words lets say multiply what you know by 10.
Now textured is as broad a subject as the entire field of modeling, just however usually considered harder than modeling especially because to get modeling going one usually skips the part where you design at modelling stage how the uvs are going to react, making uv mapping unnecessarily hard
Wait 3 years then you dont need to layout uv's, your not the ONLY person who curses texture coordinates to the lowest pits of hell. Almost everybody does including Disney.
is it essential to use the uv texture editor or are there other ways?
yes you need to uv map, you can also try to work blind if you wish. But yes there are other ways tough not necceserilily available for you, since that would mean you would need to forego using normal 2d textures and use something like Ptex.
http://www.disneyanimation.com/library/ptex/
or is that impractical with a character as they are always square?
Now this contains two assumptions. Yes textures are always square however they dont have to cover a sqyuare area. That's why you lay out uv's.
