What are you having trouble with? If its just the general system, I'll try and condense it as best I can.
Basically, the "actual election" is voted on by members of the Electoral College, who are selected by their party, and for all but 2 states must vote the way the popular vote goes. In this way the president is only indirectly elected by the people, and its possible to win the popular vote and still not become president because of the way the votes are spread out (Happened in 2000 in fact, so its not some weird thing that happened back in the 1800's even)
Thoughts on it... Well, thats a personal matter. There isnt any real objective way to look at it, although I tend to favor a popular vote myself. The criticisms are pretty obvious, and Al Gore can tell you the biggest one, which I mentioned above (getting the most votes but still losing)
It also gives a slight advantage to small, less populous states. For example the most populous state might have 10x the population of the smallest one, but only 8x the electoral votes (and likewise, they share the same number of senators, and a similarly skewed number of congress members). As before its up to you to determine if thats good or bad.
If you can't tell, I'm generally against it, and think MAYBE it served some function in the past when information wasn't as readily available, but today it is antiquated and obsolete.