Q&yourA: Buying a house (in the US)

A long-time reader asked me to ask you all how to buy a house. Her story: Single mom, got a job an hour away over the state line, and can now afford to buy a house in the new location. But she has no idea how to start. She belongs to a credit union in her current location, which is in a different state from where she'll be buying the house.

All I know about this is that you need to get a mortgage preapproved before you start looking at houses. But I don't even know where you go to do that. Can she do it from her credit union? Does it matter that it's across a state line? Do credit unions even do mortgages, or only banks? And then what does she do after she gets a mortgage approved?

Anyone? If you're not in the US, please feel free to explain to us the process of buying a house where you live.