Hi,
Can I just get on any train in the country and pay by card once on the train or do you have to buy the ticket before you get on? If so do they take credit cards (Specifically Amex)?
In general, you must obtain a valid ticket for travel at the first possible oppprtunity. If you choose to pass up the opportunity, various things can happen. Some companies will only allow the purchase of undiscounted tickets on board. Others will issue a Penalty Fare which is twice the undiscounted fare or £20, whichever is greater. You may even be prosecuted for failing to produce a valid ticket when requested, which would result in a fine and possibly a criminal record.
Sometimes, it is impossible to obtain a ticket prior to boarding a train. In this circumstance, you can buy a ticket at the first opportunity without any penalty. This may be on board the train, or at the destinaton for example.
I use American Express and have never had a problem using it to buy a ticket on the railways.