When I was in grade school back in the dark ages, we learned this song to learn the states. I still use the middle part of the song to help me remember all 50 states (and in alphabetic order no less). Now thanks to youtube, you can even learn them by where they are since this video highlights each state on the US map as it calls them out.
For me, after I knew all the states, it was much easier for me to learn the capitals.
And an unimportant anecdote to add. We have a group of friends that go to a nearby restaurant/bar and play trivia on Wednesday nights. Last year, they actually qualified for the state finals somewhere out on the Eastern shore and came in something like 4th. Anyway, a few months ago, we decided to go out and join in since we hadn't seen these friends too much and one of the questions was the capital of South Dakota. I was able to provide that and we got 10 points for the answer. Since the team only won the night by 2 points, I was pretty proud of my contributions (I actually got 3 out of 20 questions that no one else knew).