To wear or remove clothing use either right click the item in your Inventory or, for taking off only, right click on your avatar and select Take Off from the Action Wheel. You can also choose to wear clothing found in the world. This can vary from a dialog box offering to let you wear anything chosen immediately or by right clicking and selecting Wear from any menu.

You can only wear one type of item at a time. For example you can have on pants, shirt and jacket but not pants and 2 jackets. You do not need to take off the worn item, wearing another will replace it without asking.