Clicker training is the way to go. You can look up the basics on Google or Youtube-- I believe ErinsAnimals recently posted a video about how she clicker trains her dog... It's the same with rats, and you don't even need to buy a clicker; any mouth click or distinct sound will do.
I thought about clickers, but as I often take our true shoulder rats outside, I might not have one with me or our rat might be too far away to hear it, and it's just so much more impressive when people watch your rats respond to voice commands.
But clickers do have a distinct advantage. You see, I've discovered that rats are very specific in the way they understand commands and human language in general. For example, we tried to teach Fuzzy Rat 'Stop!' for almost two years to no avail. Then one day I shouted 'Fuzzy Rat Freeze!" and she froze in place... She had heard the word stop so many times it didn't mean anything to her, but "Freeze" meant stop and it worked a treat. Also she was used to hearing her name 'Fuzz" or Fuzzy so often it had lost it's meaning.... Her full name Fuzzy Rat was associated with a command that was to follow, so all commands had to be addressed by starting with Fuzzy Rat or she wouldn't respond, then a precise command phrase had to follow... So, "Fuzzy Rat up on hand, or Fuzzy Rat come to daddy were commands, whereas up on hand or come to daddy were human noises she simply disregarded like all of the other things we said. If you think about it people talk a lot and most of it is irrelevant to our rats. How is a rat to tell if you are talking to her or about her?
Clickers are good because they can be associated with specific commands or communications. Three clicks means dinner time, two clicks might mean come, etc. There's no confusion.
On the other hand, rats can learn your tone of voice too. So they can gauge the urgency of a command by how loud it is for example. So when our rats are doing something really stupid and I shout a command to save their lives they respond faster and more regularly than if I just call them for skritches.
So a clicker is good because it's very specific sound your rats can recognize and differentiate from normal background human noises. Even the name you call them can be command specific. When I say Cloudy Rat come to daddy, Cloud comes, when I say Misty Rat come to daddy, Misty comes. Come to daddy... is just background noise to both and no one comes.
If you are very precise with your vocal commands you don't need a clicker and the tone of your voice will set the urgency level for your command, on the other hand a clicker is a very easy sound for your rats to interpret as a command, just don't misplace or forget your clicker at home.
I start with their names, then "come", "spin" and "shoulder" commands. I just use rice krispies to guide and reinforce their behavior.
I've been doing some research on clicker training recently since I'm hoping I can use it to help get my rather hyper/skittish rat to focus better and have more training options. From my understanding, a clicker is used only as part of the training process, so once the rat learns the cue the clicker doesn't need to be used anymore. Since it is always used in conjunction with a treat, it is a reliable way of telling the rat that they have done a good job and that they deserve a reward.
Here are a couple helpful sites I've found that describe the process:
When you clicker train you also use voice commands... that's how it works. You start off with click and treat, then move to click only when they do what you want them to do and treat only if they do the action. Eventually you start saying the command when they do the action while also clicking and then treat... then eventually they've got it and you can get them to do the action by command only without the click. I have never clicker trained a rat yet but I have clicker trained a dog I used to have and my cats.
Like KitKatzRatz said ^, when you clicker train, the sound is a marker to communicate with the animal. So once you teach them the trick and the voice command you don't need to use the clicker anymore. I'm not very experienced with clicker training, but it seems like the best method. Here is a really good website by an experined clicker trainer with lots of good info about clicker training (check out her videos too!): http://www.useyourclicker.com/the-rats.html
Before you start training you need to bond with your rat to gain his/her trust and make sure that he/she knows his/her name. In my experience, "Come" is the best command to start with as it makes future training easier.