I started to teach myself last summer which was the summer between my high school geometry class and algebra II (which I'm in now). I would say know how to work with trig and be reasonably comfortable with it (know all the identities and that junk); as for algebra, it helps to understand logs and e. Being weak in trig and logs was what hurt me the most when I first started but if you've mastered those it shouldn't be too hard to work your way into calc (as long as you work hard). I would recommend not starting off with rigorous books and textbooks at first, start off with a fun one or two that shows you what you're doing and why (like The Complete Idiot's Guide to Calculus, Calculus the Easy Way, or Calculus Made Easy). Once you're reasonably confident you have some idea that you know what you're doing (i.e. you can take derivatives and antiderivatives, etc) then move on to something more rigorous. And remember, as that Calc Made Easy book says, "What one fool can do, another can."
