The thing is, you can't really make a universal tutorial that would cover everything, even if you constrain yourself to only using FCEUX. Not all games work the same way, and some have peculiarities that require special actions to properly map them; things like animated tiles, shifting color palettes, unreachable area, background tiles that are not fully on screen, finding the exact starting point of moving sprites, etc.
(This should really be in the Mapping Tips/Guides forum)
We can try and give you some tips and tools, but as in all things, experience is the best teacher. Your first few maps will probably be terrible and most likely riddled with errors. That's okay though, we all started there.
Okay, let's start with, in my opinion, the very basics. In FCEUX, you can enable/disable both the sprite layer and the background layer (though I don't remember the default keyboard shortcut for it). By default, removing the background leaves only black, and since black is used on most sprites, that makes it impossible to accurately "cut them out". To remedy to that, edit the fceux.cfg file in your FCEUX directory, search for the string "gNoBGFillColor" and change the 3 digits number after it to "100". This will change the overscan color (that is, the color displayed when there's no color specified such as when you disable the background) to a lovely pink.
(And if you're unlucky enough the sprites you want to capture feature the same pink color, then play around with the number in the config file)
Hopefully, you understood the procedure I just gave you. If not, there is likely no tutorial complete enough to help you and you'll just have to try it alone for a while to get some experience.