Once you have some Coins, go to any of the ourWorld Clothing Shops to purchase some clothes for your Avatar. You can find the shops by exploring the world, or you can use the Menu in the upper left of the screen then select "Shops" from the drop down that appears.
You can only buy clothes that you have enough Coins or Gems to afford the item and are high enough level to wear it. (Note: Most items you buy with Gems can be worn at any level.)
To buy an item, select it, then click ADD. This adds the item to your cart.
When you've selected all the items you want to buy, then click Checkout.
If you're happy with the items in your cart, click Buy Now. Otherwise you can go back into the store to add more items or click the X next to the item to remove it from the card.