What is the best way to travel to Liverpool or Edinburgh from London? I would imagine the train, but I’m not sure the best way to go about it…

As the post says, I will be in London in August and want to see Liverpool and Edinburgh. I plan on taking the train, but thought about renting a car. What is the best and cheapest way to buy train tickets? Is it easy to just hop on the train? Any advice would really help. I’ve never traveled by rail in the UK before.