1. You need some bitcoin. You can use Circle, Coinbase or Localbitcoins to buy BTC. I use localbitcoins.
2. You need a wallet to keep the bitcoin in. I'd recommend Electrum for a first try.
3. Buy the bitcoin from your chosen market and have it sent to your wallet address (you'll be able to find this in your installed Electrum wallet).
4. Download and install Tor Browser Bundle if you're trying to keep things simple. For max security people use Tails OS (which is an OS you install on a USB stick, it forgets everything you do every time you boot up so there is no evidence of anything) but if we're talking a one of small purchase to test the waters Tor Browser Bundle will be fine.
5. Find the darknet market address you want (eg alphabay, dream market, oasis etc). Use a well trusted site like deepdotweb to get this address. If you use a dodgy site to get the address there is a chance the address will be a fake mirror and your password will be phished and your bitcoin stolen so this is important! Use a trusted site to get the address and bookmark it. Do NOT use links people posted into this forum if you value your money.
6. Register on the darknet market of your choice.
7. Log in and buy whatever. When you send the vendor your name/address make sure it's encoded with their public PGP key. There should be a check box to click to ensure your address gets encrypted. If you want to write/receive long letters expressing your undying love to the vendor filled with personal details then you'll need your own PGP kleopatra setup. Use this tutorial to set it up:
https://www.deepdotweb.com/2015/02/21/pgp-tutorial-for-windows-kleopatra-gpg4win/
8. When your shit arrives log back in and "finalise" your order. This confirms that you got your pack and then releases the funds into the vendors hands. If you don't do this the vendor will have to wait 30 days to get their money (called auto finalise) which can be a pain for them.
If you're going for max security you should consider "tumbling" your BTC before you transfer it into your darknet market account. For a small first purchase I wouldn't bother but certainly if you're thinking of buying a lot then I'd tumble. You basically transfer your coins into a tumbling account, they mix the coins with other people's coins, and send you back the same amount. The bitcoins you bought from localbitcoins (or wherever) can no longer be linked to you.