Most of the manufacturers have their own specific cleaning procedures. A typical one calls for cleaning monthly. It's a two-step process on those I've looked at. Essentially, you fill the tub, add one chemical, run it to dispurse it throughout the piping, let it sit, drain then repeat with a different chemical. Some of them have a cap you can remove to add the chemicals from above, some you add to the tub basin itself.
I think I've seen 'caps' for the jets as an aftermarket item. No idea if they work, or how well, or if they are model specific, or if I'm remembering correctly!
This type of tub can get pretty nasty if you don't clean it and plan to use it regularly. one reason why many of them are there for looks after the first 6-months or so, people don't want to take the time or spend the money to deal with them.
Personally, I use an air tub...the advantage is that it blowdries itself after use, and since you're not circulating water, crud doesn't get as deep into it. It still takes cleaning, though. I pour in some bleach and dishwasher soap, let sit, cycle it a few times. I do not think this would be sufficient for a water jetted tub, though.