There's documentation in there(expressions) that covers all the basics, but there's also a bit of an assumption that you've done some expressions before, be it in mathematics, programming, regex, whatever. There's reference, but little in the way of gently easing you into expressions in general. More often than not, it's silly syntax things like a missing bracket - but you need to know how to read an expression to find it.
I strongly recommend that if this is becoming overly frustrating for you that you try using CHOPs instead of expressions. That's precisely what it was designed for: to allow people who aren't comfortable writing great long expressions to use a network based channel editor…this also gives you the advantage of being able to see representations of your expressions in a graph. Writing expressions is great if you're used to it, especially for a quick and dirty solution - but CHOPs gives you more structure and control at the expense of a little more setup time.
Using expressions within a complicated app like Houdini isn't really the best place to learn math expressions…

Alternatively, if you have a specific example of something you're struggling to solve, I would suggest posting it here and I'll bet several people will jump all over it…

Cheers,
J.C.