I ran a whole bunch of Ethernet this week in my house. Everything depends on how your rooms are setup. In my case, I had my Dish Network installer bring coax cable from the dish into my living room through the garage and up through the living room floor behind my TV stand. I used this hole to get my Ethernet cable down into the garage, where I could feed it through into my basement.

Then, from my second floor, I used an electrician's fish tape to pull the wire from my basement up to the second floor on the side of my laundry chute. The laundry chute was handy because it goes from 2nd floor to 1st floor to basement, and there was a nice big gap between it and the surrounding wallboard, which made fishing the wire relatively easy.

If you don't have a laundry chute, maybe you can find a closet that's above another closet where drilling larger holes in the floor won't be a big deal.

A less invasive option would be to use power line Ethernet adaptors to bridge the gap between floors. I think those top out at around 4mbps (at least they used to), but are probably more stable than wireless (haven't used them myself.)

Running cable between rooms on the same floor is pretty simple. You can sometimes get it under or behind your baseboards, under the outer edge of wall-to-wall carpet, etc. Failing that, you can use some rounded cable raceways to hide the cable, but those often just bring more attention to the cable. If you just have to go through a doorway, I'd drill through the wall next to the doorway and patch the holes whenever you need to move it. I'd avoid wires going through the doorway itself if possible.