It's simple to create lists and cards but I have not found a way to move a card from one list to another.
How do I move a card to another list in Trello on the iPad?
I can't tell for sure if you're using the Trello website or the the Trello iPhone app, though I'm assuming it's the web site, given the context.
I recommend you use the app, however. It allows you to tap and drag cards left and right, to different lists, and that works well.
Note that when you click on a card to open it, you can click on the list name, to open up a couple of spinners, to move to a different list, and a different position. However, in my experience, that bit of the user interface is annoyingly buggy, and I gave up using it.
(I just tried it again, and in one of my three attempts, the item I was moving disappeared completely!)