Step 1: Make your offer. What kind of shiny pokémon are you selling? Also, only registered sellers can make offers, so register if you haven't yet.
Step 2: Wait for a seller to accept your offer. When they do, negotiate a common time to go online. Then exchange trainer names, and a combination of 3 pokémon for the Link Code feature of the game.
Step 3: Go online and trade. Make sure you matched with the correct trainer, as the Link Code feature only matches codes. Other players could happen to use the same code you set, making mismatches a common occurrence. Be patient and try again until you match with the buyer.
Step 4: Get paid once the buyer confirms delivery.
Step 5: Enjoy your profits!
Other than shiny or strong pokémon, can you sell items as well?
Unfortunately, there are no Pokémon Let's Go sellable items for player-to-player trading. The game doesn't feature hold items, which can accompany traded pokémon. Candies are a stretch, but if you (and your buyer) are willing to trade off/transfer quite a large number of duplicates, you're free to do so. There are many items that can be sold to NPCs however. Items with a description that includes ‘can be sold at a high price to shops' are worth many pokédollars.
At any rate, here at PlayerAuctions, you've got security, safety, and reliability all in one place. It's the best player-to-player marketplace you'll find, so get selling! You'll be swimming in your profits soon enough.