Cat training, like with dogs, depends on temperament and motivation. Some breeds are known for being easier to train, like Bengals or Siamese cats.
Food motivation can be promoted by having a strict feeding schedule. It makes it easier to use regular food instead of fattening cat treats as a "treat."
Teaching a cat "Sit"
If your cat is motivated "sit," is a pretty easy trick for a cat to learn. Using a treat, hold the treat over and behind your cats head until he sits. When he does sit, say "sit." Repeat this process, several times throughout the week, then try getting him to sit, by just using the command while he is aware that you are holding a treat.
Eventually you may be able to have your cat respond to the word "sit" without external motivation.
Teaching a cat to fetch
Fetch is a one of the more rewarding tricks you can teach your cat. Everyone I showed that my cat could fetch was impressed, and the cat loved the game and would even request a play session.
The most important aspect of being successful with fetch is to use a toy that your cat can actually carry in his mouth. Tiny plush mouse toys may work, but I've had the most success with mouth sized crumbled balls of paper and hair tie rubber bands, but be sure to put these away after play to ensure that these things are not eaten!
1. Test their interest with the right toys
First, you need to gauge your cats interest in a play session and have a good stockpile of throw toys (paper balls or hair ties). You will know your cat is interested in playing if your cat chases after the throw toy and bats it around. Paper balls are great, because they make noises. Rubber band hair ties bounce and are easier for a cat to carry in their mouth.
2. Throw lots of toys and let your cat chase the toys
When your cat loses interest in the throw toy, after batting it around, throw another.
The key here is making the game the motivation. You want the cat to learn that they can get more things to chase if they play fetch. You want to give them a steady stream of things to chase.
3. Keep throwing toys and reward your cat when a toy makes it back to you by throwing the toy again
Patience is key here, because you want your cat to bat the throw toy back to you. When the toy gets back to you, you can throw it again.
Eventually your cat will learn that the toy is much more fun when he brings it back to you, because he gets to chase it when you throw it.
If your cat is food motivated, a treat each time it brings back the toy may help encourage the process. However, in my experience, a cat that is already motivated to play will be interested in the better play experience.