Cat fights aren't pretty, and understanding why your cat gets into fights is the first step in preventing it from happening again. There are a number of reasons which may be contributing to this but there are also solutions to help.
Cats are generally very territorial animals, and they will fight another if they want to be the alpha. This is quite common in a highly cat populated area. For example, if you have have just moved into a new house your cat may get into a fight the first time they are out and about. This is them adjusting to the existing hierarchy in the area, they need to find their place in the neighbourhood.
Male un-neutered cats are more likely to get in a scrap than ones who are neutered. This is because of breeding partner competition. If there is a female cat in heat, this can cause severe fights and something to keep an eye out for as it could lead to some nasty damage.
The wider your cats territory, the more cats they are likely to come into contact with and therefore, more potential fights to ensure they remain the dominant cat throughout the area. It can cause a lot of distress if a neighbour cat enters your garden, if this happens it would be good to speak with the cats owner to see if this can be resolved.
There are solutions to help everyone get along. Investing in a cat containment system means your cat has free reign of the garden and has their own guaranteed territory. It can stop other cats entering the garden too, which means no fights at all.
Neutering your cat will also help as this will take away the desire to find a breeding partner, which should take away the need to fight another cat.
Be sure that your cat is up to date with all vaccinations. As most cat fights can be quite nasty and leave puncture wounds, you need to ensure your cat is protected against FIV and other cat related diseases.
Get advice from a qualified cat behaviourist. They have heaps of knowledge and could potentially help calm your cats down. Advice is especially useful if your indoor cats fight with each other.
Never try and break up a cat fight with your hands. This could result in a lot of scratches bites, if this happens you need to immediately wash the wound with anti-bacterial soap as cats mouths carry a lot of bacteria! The best way to stop them is to squirt water on them, throw a blanket over them or try to re-direct their attention.