The Dispensary
Starting at level 9 you will have access to the Dispensary. You'll need to collect certain upgrade items to unlock it.
Once your Dispensary is unlocked and you've accessed it, all you have to do is select an empty slot, and then pick an item from your Warehouse or Shed (you can use the tabs to change between the two). After selecting an item, you can adjust the price and the amount you want to sell on the right-hand side, and then click the Sell button to pop it into the slot. Players will then be able to buy the items from your Dispensary through the use of their Global Market.
The Global Market
At level 15 you can unlock the Global Market. Viewing the Global Market will list for you a series of random player Dispensaries, each with their own set of goods that you can buy. Although you will only see the top selling item on display in the Global Market, selecting the item will open up the Dispensary of the player which may display other items they are selling as well, so it's good to check all Dispensaries if you are in need of a particular item or material!
If an item is greyed out and you can't purchase it, that's because you either haven't unlocked the item yet, or it's already been sold. Once you unlock it (e.g. breed it in your lab, or build the production factory that makes it), you'll be able to buy it in your Global Market as long as a player still has it in stock.
Global Markets refresh a new list of dispensaries on display periodically, or you can rush the refresh by spending diamonds or watching an ad. Be sure to check back often!