Your inventory (suitcase or shirt icon, or CTRL+I) is where everything you own in SL lives. All that you ever possess in SL will be in your inventory at some point.
You should arrange things into folders, since that not only makes it easier to find things.
Inventory objects can be manipulated by dragging and dropping, or by right-clicking to get a menu.
Common inventory menu terms:
Wear - Put the object onto your body, you can also sometimes specify where the object will be attached (hand, food, etc.). Wear also removes whatever was currently in that slot on your body.
Add - Same as Wear, but does NOT remove whatever was already in that slot. Note that this can cause issues if conflicting items are both attached to the same point, so use with care.
Delete - removes the item from your inventory. NOTE: use with caution as you may not be able to undo this action.
Copy/Cut/Paste - if an item can be copied, this allows you to do so. Just like copy/cut/paste commands on your computer, you cut or copy from one place and paste into another. Very handy for making multiple outfits of clothing.
Drop - takes the item out of your inventory and drops/rezzes it on the ground.