You can access your inventory by clicking the My Stuff button at the top right of your screen. Your Inventory window will appear. You can toggle your menu open/closed with this button as well.
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Your inventory will fill up with all sorts of things much faster than you'd expect. It's a good idea to start organizing it right away, before things get out of hand, messy and confusing.
To organize:
In your Inventory (accessible by clicking the My Stuff button), you can search by keyword in the white text box. The search will retrieve items in your inventory with that word in the name.
To give something to someone via profile:
In your buddy list, click the I icon, which will access your friend's profile. Drag your inventory item to their profile.
To give something to someone nearby:
Drag the item from Inventory and drop it onto the other Resident's avatar.
To give something to someone in your Calling Cards folder:
Drag the item directly onto their calling card.
If something is not loaded in your inventory, there could be a few reasons. Your internet connection might not be robust enough to load everything at that current moment. This has a high probability of happening on a wireless or satellite connection. You might also want to clear your cache. Access the Preferences window, go to the Network tab, and select the Clear Cache button.
When you receive an item, it will be moved to your inventory. However, you'll often have to open it to unpack it and be able to either wear or use what you've bought. Drag the inventory item to an area beside your avatar. It will display a box. Right click the box and select Open. The contents of the object will be displayed in your screen, and you can either Copy to Inventory or Copy and Wear. After you've copied, you'll want to clean up after yourself. Right click the box again and select Take.
You will generally have to open the box and unpack it to add to your avatar, instead of simply wearing the item.
When you buy an item and it shows up in your inventory, drag the item to an area next to your avatar. Right click the box, and select Open. Click either Copy to Inventory if you don't want to wear the item at the current time, or Copy and Wear if you intend to wear immediately. After you've copied, you'll want to clean up after yourself. Right click the box again and select Take.
Making an object appear in-world is called "rezzing".
Here are a couple reasons for being unable to rez an object: