There's a lot of variables here.
Are the transmitter (Tx) and receiver (Rx) allowed to talk to each other? If so, then this gets easier. We know radio waves travel at the speed of light in air so then distance = speed x time. You record the time the signal is sent and the time the signal is received; the difference is the time it took it to get to the Rx. Multiply that by speed of light in air (almost a constant, if you really wanted to get picky you could measure the temperature and get the exact value) and you know distance. But this takes very precise measurements. Light travels very fast and your equipment has to be spot on otherwise your margin for error is huge.
Power calculation is best done at the Tx end... it's kind of possible to measure as a Rx, but it's not as accurate. What kind of waves are you collecting? Ground, air, sky? Anything that goes into the Ionosphere gets tricky/not reliable as far as calculating power to transmit. Also what band are you collecting? HF, VHF, UHF? All of that plays into how successful you'll be. This isn't an easy thing to do.
But all of that said, I wouldn't use an Arduino to do this. You need serious antennas and I wouldn't have the slightest clue how to hook up a DF array to an arduino. You'd want a laptop with dedicated software.
This is a big endeavor here, not a weekend project and it requires a lot of knowledge of the electromagnetic spectrum, along with some physics knowledge and math that I wouldn't call necessarily hard, but it's things you wont find in a high school math book at the local library. I would suggest finding a local ham radio operator and asking to have them explain their gear. Most hams love talking about their gear, then after you get on their good side ask them about finding distances and power to transmit from somebody else's antenna.