OK you can cut on the red line below at any place you see a pair of oblong copper pads. Each 2" section of the strip contains 3 leds and one resistor (the black thing) in a small series circuit. You have to cut only at the pads, in 2" increments.
So lets say you want 10 sections, 30 leds; just cut at the 10th pair of pads. Each section of 3 leds will draw about 3-4 ma of power, so judge accordingly. And yes you can solder wires onto those pads. Observe polarity when hooking up the battery. 
Rod
