Yes, i've taught lots of cats to do "tricks". It's quite easy provided that you take account of the following:
Let your new cat settle in for a few weeks first, so you can get to know each other before you launch into training.
You need to find something that will motivate your cat to try certain behaviours, so I strongly suggest that when you get your new cat, you try some hand feeding with very small, highly palatable treats that he/she doesn't get at any other time.
Once your cat is used to getting these treats from your hand, then you need to introduce it to a clicker. This is a small device that makes a click when you press it, a unique sound that your cat is unlikely to hear at any other time. Before you start using it on your cat, get a good book on clicker training & familiarise yourself with the technique & how to use it. Karen Pryor's book on Clicker Training Cats is very good ~ available from Sunshine Books Inc via Amazon. There's also a video to show you how to do it.
Then you start to click just before you give a treat so the cat starts to associate the sound of the clicker with getting a treat.
Once you have done that then you need to "shape" the behaviours you want by getting small approximations towards the final behaviour, e.g. "sit", "follow me", "high 5s", jump over a stick, etc. Karen Pryor's book shows you how to do this.
Training sessions should only be for a few minutes at a time as cats quickly get full up with treats & will no longer be motivated to keep trying, so just 3 or 4 minutes twice a day is enough.
At the risk of stating the obvious, cats are not little dogs so will not be motivated to try the same behaviours as dogs. You need to think about behaviours that cats are biologically pre-disposed to perform, e.g. swatting something with a paw, climbing & jumping.
Don't use toys in training sessions ~ toys are used for predatory practice & whole different neurological processes come into play that are not conducive to learning something new. Keep training sessions calm & quiet.
Set up training sessions so that the cat can be successful ~ unless they can do something to earn a reward, they will not be motivated to keep trying. So keep it simple to start with.
To train your cat this way, you really need to know about associative learning & I can't stress highly enough that you need to do some research & reading into clicker training BEFORE you start. Once you master the art, then the sky's your limit!
Very good luck with it ~ it's a wonderful way to provide fantastic mental stimulation for your cat & build a great positive bond with your cat.
If you get stuck or want to know more, please feel free to PM me.