My two cats are clicker trained
You can train anything with positive reinforcement and operant conditioning. I've trained alligators, chickens, possums, bats, cats, dogs, horses, cows and monkeys with operant conditioning. Something to keep in mind is that the noise from the clicker might frighten the cat so you can use any novel sounding device or even just verbally marking is usually sufficient. I use a whistle for my cats but they know a clicker too, the whistle just keeps my hands free.
For treats/rewards my cats are crazy for freeze dried salmon and freeze dried chicken. It's a perfect reward because I can break it into small pieces. You don't want to use something that takes too long to eat because the animal might loose interest. I found with my cats that the normal cat treats weren't motivating enough for them but your cats might be different. I only use their freeze dried treats for training and that way they are always exciting. You can use a small spoon with some wet food too.
Load your marker as described above. Doesn't usually take too much time. Cats have short attention spans so keep your sessions short.
Decide what behavior you would like to shape and write a plan. Then use your plan to shape the behavior. Use your clicker to mark when the cat is close to the behavior and keep building.
I'll admit, I use a lot of lures and baiting for my behaviors because I get results faster, but make sure that you remove the lure and the bait before you mark the behavior complete.
I target train everything first because the target is useful for shaping almost every other behavior! My target for the cats is a green furball on the end of a skewer. Doesn't have to be fancy. Target for my cats means they touch their nose to the green puff. Touch means they put their paw on the green puff.
Quick Sample shaping plan for "Target".
BR=Bridge and reward (click treat)
BR when cat looks at target
BR when cat gets close to target
BR when cat touches nose to target
BR when cat touches nose to target and holds nose to target for 3 secs
BR when cat touches nose to target, and holds nose to target for 3+secs
BR to desired length of time
Introduce the command "Target" to behavior
BR when cat touches nose to target when asked
eventually you'll want them to be able to do several behaviors without being rewarded. The click marks the behavior as being complete. Don't do away with rewards completely or you make it not as fun for them. There is no harm in rewarding every behavior for just your basic "want to have fun" training routine.
I use the command "hold" when I want them to keep their nose on the target and Ok is their release.
My cats do quite a few behaviors but I'm always looking for more ideas.
Both my cats will:
Target and Touch (and hold)
Scale on command (sit on a scale so I can weigh them)
Sit and stay (not very long)
"Find your mark' (remote targeting to a butter lid)
Give paw or high five
Crate on command
It is very possible to train cats and it is very rewarding for both them and you! Have fun, there are lots and lots of resources available if you want to really delve into cat training.
For a good read on clicker training and animal behavior in general, check out Karen Pryor's Don't Shoot the Dog. I've read it several times and it is a must if yo uwant to get into any animal training.
Have fun and Good luck!!