This is a hard question to answer, because the answer would depend a lot on personal aspects of your situation, but there are some general points of advice one can give:
(1) Try different books. It may be that the particular textbook you are using
doesn't click with you, but for classes like algebra and other pre-calc courses,
and calculus itself, there are hundreds of texts available, and some may fit with you better than others. If you go to your local Borders or Barnes and Nobles, there will be a shelf of math books devoted to these topics, and you could look through some of them and see if they suit you. Also, your college library will have lots of books like this too, which you can browse through.
One thing to remember is that different books might be good at different things: your textbook probably has lots of exercises, and you will be able to find other books with lots of exercises. But perhaps you can find different books which don't necessarily have as many exercises, but have better explanations. So you can try to combine different books: some you read for their explanations, others you use for their exercises.
If you do use different books besides the one in your class, remember that sometimes the notation may be a little different, although in precalc and calc books, most terminology is standard: sin, cos, tan, conic section, polynomial, etc. will all mean the same thing. (But some books will use notation like $\sin^{-1}$ for inverse trig functions, and others will use arcsin, etc.,
instead.)
(2) Practice basic algebra: It is very common, when students make mistakes in precalc or calc classes, that the source of the mistake is weakness at algebra. Practicing algebra will help with everything else that you have to do in math. The skills will be directly useful, and lots of other manipulations you will have to do in more advanced classes will also be similar to the skills you build up by practicing algebra.
(3) Practice with numbers: If you don't think about numbers much in general, you will have trouble with other things in math, because you won't be able to relate them to concrete things. E.g. when you plot a graph like $y = x^2$, you want to be able to easily realize that a point like $(12,144)$ is on the graph because $12^2 = 144$, while $(11,120)$ is not on the graph (because $11^2 = 121 \neq 120$), but is pretty close to the graph (because $121$ is not all that far
from $120$). Day-to-day life gives chances to practice arithmetic; try to take advantage of them.
(4) Try to learn from your mistakes: One advantage of mathematics is that when you make a mistake, there will be a specific reason as to why; i.e. there will be some particular thing you did wrong. Try to find out what it is in each case, and resolve not to make that mistake again.
One aspect of this is that math should make sense. If it's not making sense to you, i.e. if you can't work out specifically what you are doing wrong in a given situation, try asking your professor or tutor again.
One thing that can happen, because of the cumulative nature of mathematics, is that several confusions can become combined in an answer, and then it can be hard to figure out what particular thing went wrong. In situations like this,
do your best to break the computation down into small steps, so that you can identify what you did right or wrong in each step separately.
(5) Write down all your working: Use a lot of paper, write down all your steps, make them clear so that anyone else (or you in a few weeks time!) could go back and read them and understand what is going on. If you lay out the whole chain of your computations clearly, it will be easy to identify weak links later. If you skip steps, the whole thing is more confusing and it's much harder to learn anything from it later.
(6) Try to recognize when you understand something and when you don't:
Probably arithmetic makes sense to you. When you learn another piece of math
completely, it should make as much sense as arithmetic does. E.g. a common mistake in algebra is to write $(x+y)^2 = x^2 + y^2$, but to someone who is
good at algebra, this looks just as wrong as $1 + 1 = 3$ does. If it doesn't look that wrong to you, it means that you have more work to do in building up
your algebra skills.
I wish I had better advice on how to do this. One thing you could try (say for the wrong example with squares above) is to plug in some random values of $x$ and $y$ on each side and check that for most of them the alleged equation won't actually be true; this tells you that the equation between $x$ and $y$ is wrong. (If it were right, it would hold for any value of $x$ and $y$ that you plug in.) I don't know how helpful this will be though. One thing I can say is that
people do often check their algebraic manipulations in this way: after making a complicated manipulation in some algebraic equation, they may plug in a few random values just to make sure that the equation is still correct. Also, most people who are good at algebra go back and plug in their solutions after they have solved an equation, just to make sure that they really did solve it correctly. So this is a good habit to get into (and practicing it will also help you practice your arithmetic).
As I wrote at the start, I don't know how useful this advice will be to you in particular; it is based on my general observations of students after many years of thinking about and teaching math.
