Cosmetics - Lobby
In the lobby, you can see your cosmetics by clicking on the backpack icon in the item selector menu.

You will then see a menu pop up with lots of options, you want to click on the box icon.

The next menu is where you can select each type of cosmetic to find your purchased ones.

If you would like to change an item you can either select a new one or click on the icon to remove the item in that slot.
Cosmetics - Servers
While on free servers you will need to select the skin. You can do that with these simple steps:
- Hold/Equip item (sword for example)
Enter command /skin
A menu will pop up with your options. Right-click on the skin you would like to use.