I've never purchased anything on there (only window shopped), but here are the basics:
-Download the Tor Browser: this allows you to access deepweb sites.
-Get a reliable VPN (virtual privacy network): gives you a fake IP address so you can't be tracked. There are a ton of these out there, the best ones need to be bought.
-Purchase Cryptocurrency: digital currency that is hard to track. The most popular is bitcoin.
I suppose if you're paranoid you can tinker with the Tor and VPN settings to make them more secure. 'Wash' bitcoin (I'm not sure what this entails). Get a temporary PO Box. The only other thing is finding reliable sites and vendors, I'm guessing there are people here at SS that can help you out with that.