First, navigate to the "Private Swap" button on the left hand menu and click it. You'll then be taken to the private swap screen, which looks like this:
Next click on "Browse your NFTs" to begin creating your offer. This will launch a submenu from the right with the NFTs currently in your selected wallet. You can also search (top left) or filter by collection (top right) when browsing your NFTs through this submenu. Once you've selected the NFTs to be included in your offer, click the "Add to Offer" button.
Next, you'll be brought back to the main page and the selected NFT will now appear in your offer. You can also add some WETH, to sweeten the deal, if needed. Once you're satisfied with your end of the offer, add in the counterparty's address on the right side. If this is a new wallet address, you'll need to copy and paste it in and then select the drop down that says "Create [WALLET ADDRESS]".
Click the "Browse Counterparty NFTs" button. This will launch another submenu from the right side with the NFTs currently in the counterparty's selected wallet.
Similar to when you browsed your own collection earlier — search is available (top left) as is filter by collection (top right). Once you've selected the counterparty NFTs to be included in your offer, click the "Add to Offer" button. After this, you'll once again be brought back to the main page and the selected counterparty NFT will now appear in your offer.
Once again, you can request WETH from the counterparty as part of the swap, if needed. Once you're satisfied, click on offer duration and set the timeframe after which the offer will expire. For the purposes of our example we'll set the offer to expire in 5 days.
Once you're satisfied with the terms of the deal, and the offer duration, click on the "Generate Offer" button at the bottom of the screen. This will launch your wallet and prompt you to sign to authorize the transaction. Once you've signed you'll see a message stating the offer has been created. You'll also notice a button on the bottom from which you can copy a link to the offer and send it to your counterparty through their linked social accounts, if you so desire.
Once the counterparty accepts the deal, you'll see the new NFT in your wallet. You've now completed a swap on Aspen.