Emoji chars are simply Unicode chars, just with more limited support as you progress backwards through iOS history. To enter emoji using the keyboard, iOS 5 and 6 provide the system standard Emoji keyboard (settings>general>international>keyboards>emoji). In code, any standard text rendering object will show most escaped chars you pass to them:
UITextView *example = [[UITextView alloc]initWithFrame:CGRectMake(0,0,320,460)];
[example setText:@"\U0001F604"];
[self.view addSubview: example];
Simple as that.
Note that prior to iOS 5, text rendered and sent as Emojis utilizes the iOS private Unicode space, which means anybody not on an iOS device will get a whole lot of ? And [] instead of characters. See here for the hack that enables the emoji keyboard in most of those emoji apps on the store.