There is actually very little difference between the early signs of FIP and the early signs of other common feline infections. Symptoms like sneezing, coughing, and nasal discharge can all be caused by FIP, but they can also be the result of a simple cold, or some other infection. The same goes for other common symptoms like fatigue, loss of appetite, and persistent fever.
All of these symptoms are a good reason to take your furry friend to a vet to get checked out. It might be FIP, it might be something else. But whatever it is needs to be treated. If it is FIP, it's worth noting that the disease can be treated nowadays, thanks to a new FIP treatment being developed a few years ago.
That said, I'm afraid there is no easy way to diagnose FIP at home. Even one of the symptoms that is most associated with the disease — abdominal swelling — can be caused by a variety of other, more common issues. It's better and safer to get help and let the vet give you a proper diagnosis.