There are many ways to distinguish a male from a female odonate. In general, females tend to be more cryptically colored; so bright blues and reds are the norm for males, whereas browns and greens are more common in females. There are many other features to look for as well, and I'll discuss them in this Madame Dragonfly series.
To begin, we'll compare the male and female California Darner. Here's a look at the male:
The first feature to note here is the constricted "wasp waist" at segment 3 of the abdomen. This means that the abdomen is skinniest near the base, and then widens out from there on to the tip.
Next, notice the appendages, which are shown enlarged below:
The top two, the cerci, are simple in shape, and curve upward at the tip like skis. You can also just see the lower appendage, the epiproct, between and below the cerci.
Now let's compare this with the female California Darner.
In addition to the overall more brownish color, note that the abdomen is wider at the "waist" than in the male. It gives the female's abdomen a "stocky" appearance.
Also take a look at the appendages, which are shown enlarged below:
The female has only upper appendages; there is no epiproct. Also, the appendages are "leaf" shaped, with no upturn at the tip.
It's useful when identifying dragonflies in the field to check whether you're looking at a male or a female. Indicators like the ones shown here will help.