How to maximise a window horizontal or vertically?

By default there is no such key binding (in 3.5.1, see other answer for 4.1). But you can create one. Use this snippet (or better add the key binding to your existing configuration) for your rc.lua file:

clientkeys = awful.util.table.join(
  awful.key({ modkey }, "F7",
    function(c) c.maximized_horizontal = not c.maximized_horizontal end),
  awful.key({ modkey }, "F8",
    function(c) c.maximized_vertical   = not c.maximized_vertical end),
)

It assigns horizontal and vertical maximization to mod-F7 and mod-F8, respectively.

Since awesome version 4.1 this is Mod+Ctrl+M (vertical) and Mod+Shift+M (horizontal) per default.