Many decisions we face, both in our personal lives and in the political realm, touch on scientific disputes in some way. Think of things like global warming, genetic engineering, nuclear energy, alternative medicine, and intelligent design, all of which are hotly debated by the public. Also, don't forget less politicized but equally important issues, like the future of technological progress.
In any society, especially a democracy, it's important that intelligent citizens educate themselves. Whether to spend time and energy on this sort of thing is your own choice, but if you do, it's important to learn to judge as accurately as possible from the information at your disposal (or, if you don't have good information, to suspend judgment).
So how do you go about doing this? Here are some tips.
For a start, to participate in informed discussion, you'll need to know the basics. You can probably find your way to popular books and websites, as well as to reference sites like this. Beware, though: popular works sometimes sacrifice accuracy for ease of understanding, or just for a good story. This is especially true of counterintuitive fields like cosmology and theoretical physics. In many cases, it's easy to overestimate how well you can understand subjects without heavy mathematics.
Sometimes, it pays to refer back to deeper works, written by scientists for an audience of other scientists, often specialists in the field. Often, these will be from peer-reviewed journals. Reading these will not improve understanding for everyone, but to benefit you needn't be a specialist yourself.
Many scientists have papers on their own web sites nowadays. Many are on large preprint archives, like ArXiv and CogPrints. Some journals also put papers on the web for free. There are tools like Google Scholar, Citeseer, and Scirus that can help you look for the topics of your interest.
In addition to knowledge about specific fields, there is some knowledge will help you productively read about science in general. This is especially true of statistics. Many branches of science use statistics to turn experimental results into conclusions.
A large number of web sites discuss the classical logical fallacies, which are useful to know about when things get more polemic. The same is true of cognitive biases and how to avoid them, on which there exists a large body of research. Applying these to your own thinking will help you avoid common errors.
A lazier, more efficient strategy than investigating for yourself is to find sources that you trust and follow their opinion. Look for objective indicators of good sense such as a proven track record. Seek out the best advocates of positions that you dislike.
One major bias that applies here is overconfidence. When experts in a particular field agree on some conclusion, in most cases, you will not be able to see things better. Scientists, being human, can and do engage in herd behavior. Science is not a democracy, and the majority is not always right. However, the view of the majority of relevant experts is almost always going to be a better bet than the opposite. Of course, finding out who the relevant experts are and what their opinion is can be nontrivial in itself.
Very few issues are truly one-dimensional; even in cases where you can't decide between two "camps", there will often be interesting claims that both "camps" agree on. Try to find them.
Often, things are muddled enough that you can't find out the truth no matter how hard you try. But there are systematic steps you can take to make your conclusions more accurate. On average, you and society will be better off for it.