Only work with people whose PayPal accounts are verified (getting partial payment up front allows you to check this early), you're less likely to run into people paying with stolen credit cards this way.
Only work with people who have an online presence of some sort, people who have a reputation they might want to avoid hurting. They're less likely to outright scam people, and people who intend to scam from the start often make throwaway accounts. You don't need to limit yourself to famous or "big" clients, something like a long history of non-spam posts on sites like TIGS, Twitter, or Reddit is usually plenty.
Related to the above, look potential clients up before you agree to work with them. Artists often share stories of scammy or otherwise unpleasant clients online in communities such as
Artists Beware. If the client is working with a company/studio, look that company up too, as issues with them may involve the client. Related to this, keep in touch with other artists. The best work experiences I've had have been through other artists sending those clients my way.
Don't work through services like Fiverr, these often attract shitty customers, and even when you do get paid, the rates you find there are usually terrible.
Use PayPal's invoice feature, so that PayPal has a paper trail for the fact that you were doing work for the client and that the work is complete. PayPal is more likely to take your side if you use this feature.
Lastly, be courteous and professional in all communication with the client, at all times. While that won't help with people who set out to scam you, it will avoid "scams of passion", where a client will do a chargeback just because they're angry with you personally.