The cheap and cheerfull approach is to gut an old VCR or DVD player for the UHF modulator ( the little silver matchbox were the "antena out" plugs into) this will get a signal from one room to another but not much farther.
Google will turn up some high power transmitter circuits , but check local regulations / law before attempting to use.
It all depends what you have got , then hunt down a datasheet.
If you are fortunate then it will be simplicity itself with only four pins
power,ground, audio input and composite video input.
Typically these devices will run anywhere at between eight
to twelve volts DC making it an ideal candidate for a battery powered
project with a common 9v battery.