Generally the simplest way but not the most attractive is to drill though the outside walls of the house in both rooms and just run outdoor cable on the side of the house.
They make plastic cable trays that you could stick to the ceiling or wall or whatever to protect the wire. Again it depends on if you can tolerate the appearance.
If you have carpet generally there is very small space between the edge of the carpet and the wall that the baseboards hide and you can carefully push a cable under the baseboards.
The one there is no easy solution for is doorways. Pretty much unless you drill holes you must run it on the floor.
Although ethernet is the best do you happen to have cable tv wire in both rooms. The new moca...