CSA,
the proper way to stick the slate on a vertical surface is to first prep the surface by (as someone stated earlier) stapling or nailing metal lath to the wall with a vapor barrier in between (felt paper works well). then apply a "scratch" coat of mortar to the lath. (Mortar mix and a steel concrete trowel, pressing it into the lathe until all of the lath is "sealed". (make sure that the lathe is tight to the wall with no movement, also fasten it through the wallboard and the studs. not just the wallboard. As it is setting up, "scratch" the surface with a piece of the lathe or a rough mortar brush to provide a bonding surface. Once the scratch coat is set up you can start installing the slate. Mix up a batch of mortar, but do not use mortar mix, buy portland cement and sand mix and mix it yourself as vertical stone installations adhere better if it is a little "richer" with portland cement. Using a trowel butter up the back side of your first piece of slate generously, spread it over the entire mating surface and create a small depression in the mortarwith the tip of your trowel. Apply the slate to the wall with steady pressure and a slight twisting motion and hold for e few seconds. The purpose of the depression is to creat a slight "vacuum to the slate when applied to help hold it. Once you have perfected the proper mix and your slate holds ,then start fitting the rest of the slate together like a puzzle. Take your time. Masonry is not for the impatient.once you have the slate installed and it has had sufficient time to cure, you can grout the joints with a slightly thinner mortar mix and a grout bag. Fill in all around the edges and let the mortar set up until steady finger pressure leaves a depression but doesn't leave mortar on your finger. Then strike off the mortar joints with a dull edged striking tool ( a spoon will even work) pressing the mortar into the joints and smoothing out any edges. Lightly brush the joints with a whisk broom or similar and your all set. Hope this helps some and good luck.
Mike