Place a slate in the valley so that it can be marked for cutting. Mark the bottom of the slate where it needs to be cut, then mark it again along the side.
Transfer these marks onto the backside of the slate. You always want to cut the slate from the backside, so the chamfered edge finish is on the front face of the slate.
Draw a line between the two points and cut the slate. Line the slate up at the eave and along the valley before nailing it. With the point of your slate hammer punch holes (from the backside) along the upper right side so that it can be attached with 2 nails. The new nail locations will not puncture the valley metal. Drive the nail head down so that they cleanly set in the countersinks left by the punching in the slate. Nails should not be over-driven, nor under-driven.
When installing slates along the valley, it is important to place the nails, so they do not puncture the valley flashing. Wider slates (or slate-and-a-half) are necessary to help with nailing away from the valley metal.
With your wider slate in hand rotate it 180 degrees so it can be marked for cutting. Transfer these marks onto the backside of the slate. Flip the slate over and line the mark made on the backside of the slate with the previous installed slate, while also aligning it with the scribed line on the valley. Remember to nail away from the valley metal.
