Processing inbox items
Items you put in the inbox stay there until you assign them a project or context (by using the inspector or by typing in the Project and Context columns). If you assign both a project and a context, then the next time you clean up the item is filed away where it belongs. Depending on your settings in the Inbox Processing section of the Data preferences, an inbox item with a project but not a context assigned, or vice versa, may stay in the inbox or may be automatically filed where it belongs.
Inbox items have both a Project column and a Context column. To assign a project or a context, you can click the pop-up button next to the appropriate cell to see a pop-up menu of all available projects or contexts.
Or, you can type directly into the cell. With each letter you type, OmniFocus guesses which of your projects or contexts you might mean. Most of the time you can get the right one with just a couple of key presses. For example, if you type aak or ado into a project cell, OmniFocus would find your "Adopt a Kitten" project. Once the correct project or context is highlighted, you can just leave the cell.
If you need to create a new project or context, just type its name into the cell and press Command-Return instead of Return. OmniFocus creates the new project or context for you, and assigns the action to it.
To move inbox items to your library:
For an individual action, just assign a project and a context to it, then use the Clean Up command in the Edit menu or the Clean Up button on the toolbar to move it to its proper place.
For any inbox item, including groups, you can click its handle and drag it to the sidebar or the main outline wherever you would like it to go. Drop it inside a project to add it to that project, or drop it anywhere else to turn it into a project.