It is an opamp (operational amplifier), check post #16
R1=5K ohm
R2=1K ohm
R3=10 ohm
and the LED resistors are 1 ohm (other values can be used too), these resistors are used there to ensure that the current is equally shared between the leds, not to limit the current.
The current that will go to the leds is 80mA so if it is shared equally to 8 leds each one will get 10mA, if you want more or less then R1/R2 or R3 have to be changed.
A 10K pow will work fine, connect the two ends to +5v and gnd so that the center tap gives 0-5v depending on the position.
The opamp in an integrated circuit , it is described by a model number , the one I have used is LM358 (**broken link removed**) which is cheap enough and is widely available but many others can be used.
The transistor I have used is BD139 but you can use a much smaller one like 2n2222 because the powers consumption on the transistor will be very low (less than 1/4 watt)