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The other thing sometimes called money laundering is when you have some big lump of cash that you'd rather not have people find out about. Sometimes it's an effort to keep the money from the tax man (literally the opposite of classic money laundering), other times the goal is to keep it from coming to the attention of someone else who might feel like they have some claim to the money--an ex-spouse, a creditor, the guy who owns the land where you found the bag of gold coins in the culvert.

In this kind of money laundering, the point is to make the money disappear. This is the sort of money laundering where you might make use of foreign banks, shell companies, and so on.

There are two parts to these strategies. First, you need to make the money disappear. Second, you need to make it reappear in some gradual fashion that doesn't bring it to the attention of whoever you're trying to hide it from.
Disappearing the money

The easiest way to disappear the money, especially if it's already cash (as opposed to, let's say, silver bullion or a winning lottery ticket) is to just stash it in a safety deposit box. You miss out on any investment income, but it's safe and you know where to find it.

If you really want to be able to invest the money, get it overseas. If it's an amount that you can just carry with you, buy a vacation package to the Cayman Islands or visit your family roots in Europe and take a little side trip to Switzerland or Austria or Liechtenstein.

There are plenty of fancy, complex ways to get the money overseas, that mostly require an accomplice. The most basic is an invoice scam. Establish a business that imports or exports something. Meet with your customer or supplier and arrange with him to either over-pay or under-bill, and then to have your counterpart deposit (most of) the excess into your foreign bank account. An ongoing scheme is good, because the guy knows that the lucrative cash flow will stop if you find out the money isn't getting deposited as it should, but you can also work this as a one-shot deal if your counterpart can be trusted.

Banks used to help their good customers get money discretely overseas, but nowadays there are a bunch of laws against such things, and bankers are particularly averse to going to jail for their customers. Expect them to refused to get involved and to rat you out.
Reappearing the money

Now we're basically back into classic money laundering territory.

If you stashed a duffel bag full of cash it in a safety deposit box (or under your bed), all you need to do is pull out a few bills now and then when you're heading out for a night on the town. You can raise your standard of living modestly. Alternatively, you could increase the amount that's going into your 401(k) and then use the cash to keep your standard of living about the same--gradually turning the hidden money into above-board money.

If you've got the money overseas somewhere, bring it back in some way that makes it legit. The easiest would be to create an overseas company that then hires you to do something. You do whatever it is and send an invoice whenever you want some cash. You can also reverse the invoice scam that let you get the money overseas in the first place--now you under-pay (or over-bill), while making up the difference out of your foreign bank account. A third option is a fake loan where you "borrow" the money and then simply fail to pay the money back.
Instant disappear-reappear cycles

If you can't wait to reappear the money gradually, and the amount involved isn't too big, you can always use a simple casino scam. Go to a casino and buy some chips. Do a little low-risk gambling. (For example, bet each chip, one at a time, on red. Do that 20 or 30 times and you'll have about the same amount you started with.) Get a few more chips and repeat. Play a few different games (blackjack, craps, slots). Ideally, go to several different casinos and repeat the whole process there. Eventually, cash in all your chips and go home with a story about how you won a bunch of money at roulette. Pay taxes on your winnings.