The most essential point is to never send money to, or for, or to enable, someone who is supposed to be paying you. Legitimate finance never works that way.
There are two basic attack modes here. One is that checks and electronic transfers can bounce for lack of funds, or be canceled, or be made from a stolen account, and it can take a significant amount of time for to resolve that, during which your bank will display the funds as present but on hold. If a scammer can convince you to send money during this verification, and then cancel the deposit or have it fail, they have just stolen your money. Exactly how long it takes for a transaction to clear and become final depends in part on the kind of transaction and your own bank' rules, so you should talk to them about when you can count on a deposit being final, or as close to final as it's going to be -- assuming it was legal in the first place; see the next point.
The second attack vector is that they may be trying to use you to launder illegal funds. In this scenario, the deposit is real, but is made from a criminal's account. If they can get you to send that money somewhere else, they now have money that looks legitimate, and you have participated in a crime. Illegal payments can also be canceled, and even if they aren't, you can be prosecuted.
The third attack vector, of course, is identity theft.
If you refuse to send money or other valuables, and do not give them more information than us legitimately needed to pay you (see many web articles on identity theft), then the worst that can happen is that the money you receive is fairy gold and vanishes when sunlight hits it. They can get you to waste time, and postage, but if you are careful you can limit it to that.
If you are selling physical goods, there is a risk of those being stolen, but that is part of doing business by mail order; again there are articles on the web describing what you can do to protect yourself, and what to do if a payment bounces. But the majority of scammers want your money, not your product.
And finally, I will refer you to the many existing web articles on how to recognize a scam, the kinds of scams that are common (most are variance on a few simple themes), what information you should and shouldn't be willing to give people, and how to validate a business's identity. Remember that if it sounds too good to be true, it probably isn't true, and that if they're trying to rush you, it is probably because they don't want you to think about what they're asking you to do. And remember that on the internet, in mail, or even in person, you can never be certain that anybody is who they claim to be.