Hi,
Two ways.
The first is the same way as this web site:-
Type a common text keystroke combo for a "Smiley" and it will select them.
The second is to use the Drop down indicated by the greyed out Smiley in the right hand of th Text field (In Left to Right languages)

The grey icon across the bottom indicate other panes of icons that can be used.
Around this part of the Objects pane there are some Emoji items that don't show compared with the Character Pallet version

This is missing a knife, bomb, cigarette, gun and a syringe that I remember.

8:08 pm Sunday; July 6, 2014
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad