I purchased a led circuit DIY kit as listed to find out that the parts to solder in weren't included with the board. I'm completely new to all of this and not sure of what parts I need to order to be able to put it together.

 

The first one seems fairly straightforward.

The LED driver has a couple options: LM3914 or LM3915. The opamp shown is LM258, but LM358 will be cheaper. The resistors are 1/8W. Pots and caps will depend on sizes used on the board; you'll have to measure and check datasheets.

EDIT: Just noticed it gave Digikey part numbers for the resistors and pots (trimmers).

Didn't look at the rest.