In order to make a purchase, you must have at least 1 alias, the necessary funds available in your wallet and your wallet must be unlocked prior to purchase.
Go to the "Marketplace" tab and select "Browse Marketplace".
You can look through the marketplace by going through each page, looking up an item by category or searching for a specific item in the search bar.
In a offer listing, it will show images (if any) of the item, the offer ID, seller alias, reviews, a brief description of the item, the price (may or may not include shipping), and quantity available.
Select the alias you wish to use to purchase the item and the quantity.
You can also use a third party Escrow who will act as an arbiter in the unlikely event that there is a problem with the transaction.
In the "Notes" you must include your shipping address and any other information you wish to pass onto the seller.
Once all the fields are complete and click "Buy Now", check one more time and select 'Yes' if all the information is correct.
You can find your purchase in the "My Purchases" tab under "My Marketplace" once the transaction has been confirmed by the network.