Whats is the cheapest way to get from Hong Kong to Beijing, how long will it take, and how much will it cost?
The cheapest way I know of is by train, a train leaves Hung Hom for HK every other day its the T94 or the T96 train or something like that. For a hard sleeper it costs $586 sometimes there are special offers whereby it costs $500ish (that's HK$ btw!) for a hard sleeper. Despite the name the hard sleepers aren't so bad they are about 5-6 inches of foam on a hard bunk in a room shared with 5 other people.
There are soft sleepers where you get proper sprung beds 4 per room but these cost more, or the deluxe private rooms which are shared between two and have a private toilet and shower. But these are close to $1200 thus you may as well fly.
You'll arrive at West Beijing railway station, it takes 28/29 hours depending on how long they decide to stop in Shenzhen to load up supplies. Btw you can't get off when they stop twice.
However I seriously recommend you bring your own food, since the food in the dining car at the back is atrocious. This train is run by HK Chinese which means the staff are all ass holes and they will fill general storage areas with their own smuggled goods to sell to HK Chinese people. There are hot water taps in each car so you can bring your own instant noodles. You may also want to bring your own beer as well as the San Mig they have on board are warm, expensive and San mig is pretty much piss. Western style toilets are in the disabled cars, the squat type as pictured are in the first class cabins.
Also bring your own toilet paper, the T96 train has power sockets only outside the toilets the T94 has power sockets per bunk.
To keep yourself sane the Peking opera speakers switches are hidden behind the door curtains.