There are many general symptoms that fish may exhibit when they are unwell - these are not indicative of any disease/condition in particular, but rather are general indicators of a fish that is suffering from something.
Half the battle, especially for new fishkeepers, can be distinguishing a healthy fish from an unhealthy one, and these symptoms are very important to learn and watch for.
Below are some of the symptoms of general unhapiness/stress/ill health that your fish may display. Take a moment to look them over and watch for them in your fish.
I often find that faded coloration is most visible on the fish's face and body, and in their eyes.
Above are two pictures of the same fish - at left, the fish is healthy and colorful, and on the right, the fish is dealing with a severe fin infection (not visible) and is showing faded coloration, especially visible in his eyes and snout, normally a dark brown, which have lightened almost to the color of his body.
A NOTE ABOUT
Unlike with fish who are dark or bold colors, faded coloring may be harder to spot in bettas who are naturally pale or pastel colored. With these fish, it will be especially important that you observe them and familiarize yourself with their colors and markings when they are healthy, so that you are able to spot subtle changes that may indicate illness.
While it is perfectly normal for a betta to rest on the bottom of his/her tank, the way that they do this can be very telling. A healthy, strong fish will sit upright on the bottom, using his fins to hold himself off of the ground, much like the legs of a table. However, an exhausted, lethargic or ill fish may list to one side and/or not be able to hold himself up on his fins, instead resting his body on the ground.