What if taking the train into China?

I am a citizen of USA currently in Ukraine, I am going to be taking the train across Russia and into China and will head to Vietnam or Thailand. I don't have exact dates for my arrival or departure from China but I am planning to visit a friend in Beijing who has provided a letter of invitation for a full month. Is it possible to obtain a visa with this or do I absolutely need to have my ticket to get into China and my ticket to get out?