My husband immigrated a few years ago and we were eager to get him a credit card ASAP to begin developing his credit in the States. Once he had a social security number, he had what he needed to get a credit card, but no one was eager to give the guy with the shiny new SS# a credit card. When they would run his number to do a credit check, it came up with "no history", which is, admittedly, a scary proposition for a lender.
Chase told us that Capital One's niche in the credit card market is high-risk (Read: first time, rebuilding credit) clients, so we went to them and got a secured card where my husband gave them a $900 deposit and Capital One gave him a $1300 limit on his card. A year later, when his credit was established, we asked for the $900 back and Capital One to transfer the card to an unsecured (normal) credit card. They said they couldn't do it so we closed the account and got our cash out.
At the same time we got the secured card in his name, I also added him as an user on one of my cards that had a solid payment history for 10+ years. No one knows the exact algorithm for developing a credit score, but general consensus among the articles I read was that adding someone as an user didn't do much for his/her score. We will never know what did it, but between the secured card in his name and adding him as an user to my card, his credit score four months later was in the high 700's. We were shocked that he could go from "no results" to 700+ in less than six months.