Hover over to the right-hand-side of the screen (just to the left of the grey board border) and your cursor will change to a resize cursor (double-headed arrow) along with a slightly darker vertical blue bar appearing under your cursor and the help text "Collapse or Expand the board sidebar".
Clicking here will expand/collapse the sidebar.
It looks like Trello have (very) recently included a small arrow just to the left of the sidebar to give a visual indication of where to click.
This arrow points right when the sidebar is visible (indicating to collapse it) and points left when it's hidden (indicating where to click to show it).
This is a significant usability improvement, even if you knew where to click.