Slate is a unique natural stone in that it can be cut or broken into smaller pieces, depending on whether you want a uniform tile-like material or a multilayered and sized flagstone-type material. While granite and marble tend to shatter when you break them, if you take a few precautions with slate, you can break it into roughly the size you want without fear of fracturing the stone. As far as cutting goes, there are numerous tools you can use, depending on the type of cut you need to make and the piece of slate you're cutting.
Make custom cuts in flagstone material that is roughly 2 inches in thickness, using an angle grinder. Straight cuts can be made on a tile wet saw, similar to how you cut tile material. Only use an angle grinder if the blade is large enough to cut through the stone, because a 4-inch angle grinder blade only gives you 2 inches of cutting depth.
Cut larger pieces with a plunge saw, using a stone blade. Plunge saws are used for thicker pieces of stone that you cannot cut with a tile saw or angle grinder. These saws are larger versions of an angle grinder, and their blades depend on what size of saw you have available.
Break the slate up into manageable pieces for your project. Wrap the piece of slate with an old towel and hit the piece of slate with a hammer or rubber mallet, depending on how thick the material is. If a mallet will not suffice due to stone thickness, switch over. Hitting the stone without a towel will cause it to shatter rather than break into large pieces.
Customize pieces with a hammer and chisel. While it is an old-fashioned method, it still works. Cut pieces of slate with a hammer and chisel by chiseling a line across the face of the stone where you want to cut it. Snap the piece of stone along that line, and the stone will break where you scored it. You can also create custom curves with this method.