I wonder if it's easier or harder for people who have studied several languages to pick up ASL. I mean, every time you learn a language, you have to learn the rules, like gender agreement, the importance (or lack of importance) for word order, case endings where needed, etc. (If you read the article grendel posted, it goes into that sort of thing in depth.)
A language learner has to be able (or learn to be able) to approach each language as an entity in itself, which might have similarities to other languages, but is still its own system.
ASL uses the visual orientation instead of verbal, so that would be different. Otherwise, it's the same as any other language, looks like, with its own word order indicating importance (like what Jillio said about "tense first") and so on. Maybe people who are used to starting from scratch might already have that habit of knowing that "Ok, things are different here."
In my language classes, the people who had the most difficulty were always the ones who tried to insist on translating to and from English, instead of absorbing the new language for what it was.