By left clicking on an edge between two unselected vertexes you can split it. If the edge is used by a triangle it will be split in two triangles, and if it is used by a quad it will be split into one triangle and one quad. Continuous splits can be created by dragging over multiple edges.

To make sure that the start edge isn't selected so that the reshape functionality would be invoked, look for this overlay that indicates that the edge will be split if clicked on.

When splitting edges the edges will emit particles indicating that the split is in progress

Sometimes you may want to create multiple splits of an edge. To do this tap repeatedly on the right mouse button while you are splitting to increase the number of splits.

Once you have increased the number of splits you can press the middle mouse button to decrease the number of splits. Increasing and decreasing the number of splits can be done while you make a continues split to vary the number of splits in different areas of your model.