Neil
The resistor in Harry's diagram is acting as a "current limiter". LEDs will blow (fail) at quite low current values so the resistor is there to 'protect' it.
Harry suggests 180 ohms, Dave M 390 or 430 ohms dependant on colour / type. Look up the spec' sheet for the LEDs you want to use.
If you want to experiment, (low wattage) resistors are dirt cheap. You can get a whole strip for less than £1. Start with a high value one and work down in increments until you get the brightness you want.
I've no experience of LEDs with 'built-in' resistors, but again the spec' sheet should give you all the gen' on that.
To get a particular resistor's colour code, just enter the ohms value into google and you'll get a pretty picture !
Dave