To change from cheat mode to recipe and utility mode, click the options button in the bottom left and select the mode you want.
Typing something into the search bar below the inventory will show items that have those words in it. If you were to type "coal" into the search bar, nether coal, coal ore and coal dust along with many others along with coal would appear to the right of the inventory. Double clicking the search bar darkens all items in your inventory that are not specified in the search bar. Right clicking will clear the search bar.
Pressing R while your mouse is over an item (either in inventory or in the right hande NEI selection panel) will show the available recipes for that item.
Pressing U or Shift+R while your mouse is over an item (either in inventory or in the right hand NEI selection panel) will show recipes that use the current item.
Pressing O will hide the NEI program. Press O again to show it.
In the recipes or uses interfaces, if there are multiple places to create/use an item (furnaces, crafting table, etc.) then the top left/right arrows will scroll through those options. If there are multiple recipes/usages for an item then the bottom arrows will scroll through them.