This happened to a friend of my parents. She was mostly a stay-at-home Mom and she managed the family finances, but everything was in her husband's name. When the kids were mostly out of the house, she went back to school and became a minister. She wanted to get a credit card in her own name that she could use for expenses related to church work, since she would be able to claim some of that on her income taxes.
She was turned down by every major bank, because she had no credit history herself - everything was in her husband's name. She did manage to get a store credit card with a very low, $500 limit. As she used the card and paid it off every month, they raised her limit and she was able to get a regular bank credit card.
I got one under one of those student promotions in my last year of university. Best thing I ever did - I've never had lack of credit history issues. And I only used the thing once every couple of months or so.