So.. how CAN I "train" my cat?

with my family's cats, I always followed my mom's example and used a spray bottle to keep cats off the counter or from taunting the dogs when they were crated.

Apparently and understandably, this is not a good idea.

What can I do to teach Samuel what the rules are?

I'd like for him to stop jumping on the counter.
He doesn't do it when I'm watching, but usually when I put my key in the door after I've been away, I can hear him jump down from the counter, and there is always hair EVERYWHERE.

Funnily enough, he won't get on the couch unless he's invited.

I'd also like for him to stop biting me while I'm sleeping. It hurts! I know cat nibbles aren't meant to be aggressive, but its not a nice way to wake up, and locking him out of the room has not proved successful. He keeps me awake scratching at the door and making sad noises.

From what I've gathered here, cats are not trainable in the same way dogs are, but there has to be some method of behavior modification.

Clicker training can be a viable method.
Just so you know though, ALL cats get on the counter.
If he only gets up there while you're not looking, he already knows he's not supposed to, this won't change.

I figured that might be the case with the counter.

Oh well. I guess i'm resigned to cleaning it reaaaaallllly well before I use it.

Neither of my two cats get on the kitchen counters!! I would freak out if they did, too!

We are currently using a piece of paper with packing tape doubled over so the sticky side is out to train our Hannah-cat to not walk on the nightstand. So far, it's working. We've also used aluminum foil draped over an area where we didn't want her (the dining room table at my dad's house). That worked well also. There's a spray you can purchase, something like Bitter Apple, and it's supposed to help deter cats from certain areas. Some posters used it during Christmas around their Christmas trees.

Stephanie

Try brushing him every night (or day) to get as much loose fur as possible (will also help prevent hairballs). Cats will respond to positive reinforcement of incidental good behaviour... if they do something you want to encourage, give them lots of praise and over time they will do it on purpose. Be careful using food for rewards tho', even tho' it can work, because you'll end up with a very fat cat - even little bits add up, whereas dogs can 'afford' more of those for training.

I used the double sided tape to stop my cats climbing up the kitchen drawers handles (like a ladder) on to the counters, until they got a bit older and could just jump up!

You could try putting small cups or bowls of water along the outside edge of the counter...just make sure they are made of plastic because when the cat jumps up on the counter, they will knock the cup or bowl down and plastic wont hurt the cat if it falls on them and the glass might break and seriously hurt him/her.
You could always put double sided tape along the outside edge too. That should help. My cat used to jump on the counter, we used a pepsi can with a few pennies in it with her. You shake it hard when she is doing something she is not supposed to do, and she would take off to another room. She never did it again as far as we knew. My cats now dont jump on the counter. Well, one is too small to even jump on anything lol but Peaches would jump on the counter.

I put a cat tree in the kitchen that was slightly taller than the counter. Since cats like to look upon their world, they prefer the tree than the counters. When I catch a cat on the counter, I redirect them to the cat tree.

Training isn't easy with cats because they are not motivated to please you. When they do something you don't want them to do, always redirect them to something comparable that is more appealing to them.

Scratching furniture is another problem we all live with. Get a scratch post taller than the furniture and when they hit your sofa, give them a firm no, carry them to the scratch post and show them how to use it. I make a game of it by kneeling down next to it and scratch with them. Slip them a treat if they like treats during this process.

The real key to any behavior modification is to be consistent 100% of the time.