Ysolda can be married but can’t accompany you on your travels.
When speaking with Ysolda, she will explain how she wants to learn the caravan trade to become a better merchant. Her Khajiit trader friends are willing to teach her, if she gets them a mammoth tusk. If you get one for her, she offers to teach you a bit about speech.
The easiest Mammoth Tusk to obtain is in Jorrvaskr, on the table in the left room; though you’ll have to steal it. Halted Stream Camp contains several Mammoth Tusks, if you’d prefer not to steal one; and is the location of a bounty quest.