Remember when you first learned to knit or crochet? Every abbreviation felt new and confusing, but as you got used to them, they became familiar and easy to understand. Looking at knitting & crochet charts for the first time can inspire that same initial feeling of confusion and consternation, and it may seem easier just to skip charted patterns all together, but I'll tell you a secret: once you learn to read charts, complicated patterns get exponentially easier.
The really magical thing about charts--and this is true whether you're knitting or crocheting and for both cables and lace--is that they are actually a pretty good representation of what your final piece is going to look like. And that's one of the keys to reading charts as well...remember that it's a representation of the finished piece. What this means is that if you see a symbol for a yarn over (for example) in chart row 9, you will be making the yarn over as you work that row. What you see on the charted row is what you should see when you have finished that row.
Charts come with legends, just like maps, to tell you what all the little symbols will mean. Fortunately, a lot of the more common ones are pretty standardized, and even those that aren't are generally a reasonably accurate depiction of the stitch(es) they represent. For instance, here's a simple lace chart:
Do you see how a yarn over is represented by a big round circle, while skps--which are left-leaning decreases--are represented by a line that leans to the left and k2togs--which are right-leaning decreases--are represented by a line that leans to the right? This is what I mean when I say the chart will reflect what's happening in your finished project. For example, where you see that line of circles going up the chart, you will see a line of circles going up your knitting.
Crocheters, what you'll see is a lot of ovals and lines. The ovals represent chains, while the lines will have a varying number of slashes across them to represent taller stitches:
The key to reading charts is to go from bottom to top, just as when you're making your project. Right side rows will be read right to left (again, just like working across the actual project), while wrong side rows will be worked left to right because you're essentially looking at a picture of the back of those rows. Note that some charts will only consist of right side rows, usually if all the wrong side rows are worked the same way.
The fastest and easiest way I found to learn to read charts is to transcribe them. This will help you transition from working with the written instructions you're used to while at the same time teaching your brain which symbols mean what. Before you know it, you'll be able to look at a chart and know just what your finished project will look like and how to get it there!