this is really a nebulous topic. there are so many different ways to do this with many different priducts. many connect with a molex power, so it will be powered off the psu. i think there are some that run off a usb port you have to route somehow to a port in the back of the case. i personally would prefer it running off molex power.
as for it looking clean, that comes down to you putting them in. most kits come with some clips to stick it in the case, or some strips are even magnetic. my advice is maybe get them in or near the case frame's curled edges, thats what i did with mine.
which you can
see here
that one has a pci-e slot part(so you can access the button at the back of the case) so i put it in a low slow to be further out of sight, then ran the leds down and counter clockwise around the frame of the case from there. used some black electrical tape to cover the first led so it wasnt just floating out in the air there. it came with little clips that sticky back in to the case and allow me to hold the strip in place. i like the way it came out.
others have a module that gets powered, like a fan controller, and these you can hide behind the motherboard, or in a drive bay, or maybe just in the bottom of the case if its out of view. hey, maybe you like the way it looks and want it mounted somewhere visible. maybe use some double sided sticky foam tape to hold it in place, or velcro or something if you think you'll be messing with it.
as for deciding just how you want it routed, its really down to how you want it to look, what you think looks good, and how that goes together with your systems design like light from other components or the shape of the case.
there really are a lot of nice components out there for this. in a month or two i intend to make some major changes to my components and might change my lighting. i like
the HUE+ thing, since its rgb and you can use the software to control the effects and colors. i also like the look of the box and how it can be mounted in a 2.5" tray, so i might even leave it visible.
i hope this was helpful. if you come down to putting it together and need some second opinions on routing ideas, im sure we can help with that too.