Those of us who grew up reading Walter Farley's novels would have a misguided sense of just what colic is. Colic itself isn't a disease; it's a symptom; what colic means is abdominal pain. This pain can have all sorts of causes, some more dangerous than others and some outright deadly. Telling a horse is colicking isn't the hard part, the symptoms of colic in horses are unfortunately easy to spot. Horses with abdominal pain, much like humans, don't feel like eating and will even look at treats like they're mud. Manure may change consistency, and your horse may roll around, paw at their abdomen, or shift endlessly as they try to get comfortable. Some horses will nose their flanks like we'd prod a sore tooth. Some colicky horses may also sweat even if they're not hot as a pain response.
The hardest but most important thing to do when faced with a potentially ill horse is to stay calm. Assess the situation, try and work out when your horse was last healthy, what they last ate and drank, and how long this may have been going on. Their behavior will give a good indicator of the severity of colic, but as prey animals, horses tend to be pretty good at hiding their symptoms until they're serious. Once you have a good idea of when this all started and possible causes, call your veterinarian. Vets will tell you they'd rather talk to you and examine your horse for symptoms of colic early than rush to help a seriously ill horse they could have helped far sooner.
Do your best to record your horse's vital signs (temperature, respiratory rate, and heart rate) and see what sort of gastrointestinal sounds (if any) you can hear. A horse's average temperature is around 100F (37.7C), keeping track of what's normal for your horse is a big help when they're sick!
While you wait for your veterinarian, remove the food and water from their stall. You don't want to compound any problems that may already be going on. If your horse is very agitated and won't get comfortable, walking them may help. If your horse is happy to lie in the corner and look miserable, leave them be for the time being.
In cases of minor colic, your veterinarian will probably prescribe an anti-inflammatory such as Abutazone to help deal with the pain and slow down or stop any inflammation in your horse's digestive system. Keep a weather eye on your horse and follow up with your veterinarian as necessary.