1) Don't lose the forest for the trees. What does this mean? Everything in economics is related, the concepts build on each other, if you skip one of the first chapters, then you are likely to struggle when learning material in subsequent chapters. Even if your professor doesn't make it clear, most textbooks are organized the way they are for a reason, everything builds and it is important to understand how and why the material is presented the way it is. Keep the big ideas in focus regardless of what you are currently studying.
2) Make sure you understand graphs and simple algebra.
Without these tools, any economics class is going to be a huge chore. Most textbooks have an appendix at the end of their first chapter that reviews basic graphs, their purpose, and how to interpret them. Understanding how graphs work and what they mean is crucial to understanding economics at any level. Also skim the chapter on elasticities, if the math there doesn't bother you than you are good to go.
3) Make sure you really understand the concept of opportunity cost. This concept is the core of economics, and if you have a firm grasp of it then ALL other concepts will come more easily. Prices, benefits, costs, utility, and externalities all make more sense when given in the context of opportunity costs. Review that concept here: opportunity cost.
4) Get comfortable with the idea of ceteris paribus. Not the actual Latin word, but what it implies: "everything else equal". That means that nothing changes except for one thing. In economics we like to create models (simplified versions of the real world) and then tweak one thing to see how it impacts the model. While this is not the most realistic approach, it is the best approach for beginning to understand how economics works. For a related post on conditioning your mind to think like an economist look here.
5) In economics we analyze things on the margin. This means that it is the next decision, or action, or unit of production that matters. Everything else is in the past, can't change it. But that next action/decision you have control over, and that is why it is important. This is where marginal benefit and marginal cost come into play, we care about our actions now. Get comfortable thinking about that next unit, and not everything prior. Students with experience in calculus should be more familiar with this concept.
6) Know the difference between comparative and absolute advantage. In particular make sure you understand how to solve the comparative advantage problems. Some professors go into this in more detail than others, but understanding this concept is important, and it is introduced relatively early into the semester. Review that concept here: comparative advantage.
7) If elasticities are giving you problems, then you need practice, practice, and more practice. At some point if the process of solving for and interpreting elasticities doesn't make sense then you should memorize the formula and outcomes. A better approach is to keep working problems, and talk about them with your classmates and your professor and eventually it will make intuitive sense. Another good approach is to come up with easy examples that will help you remember which elasticities apply when and what they mean. See some examples here: elasticities.
8) Understand production theory, in particular marginal, variable, fixed, and average costs. There are good tables and graphs in all books that go over this. Understanding these concepts will not work if you only memorize. Each term has a very intuitive name and directly applies to what it is doing. Read and do examples until this is obvious, as soon as you understand these different types of costs and how they relate you will realize how easy it really is.
9) Be opened minded about economics. Some people hate the idea of putting prices on everything. This is just a tool economists use to measure things. Famous economists have have used labor, water, and energy and units of measurement. Just because you don't agree with economics doesn't mean its wrong. Economics does a pretty good job at explaining individual and firm behavior. Even if you don't like it, you can apply the knowledge and tools gained in the class to better your own life.
10) Finally, practice, practice, practice. Set up a study group. Go to your professors office hours. Talk economics with your friends. Do practice problems (yeah right). The more you expose yourself to the material the easier it will come to you. You should also make this site your homepage for the semester, so every time you think about checking facebook you show up here, and remember you have studying to do!
