Fixing broken piece of concrete
The cheap way is to just go the local Big Box store and get a small bag of mortar for concrete.  Mix it up apply to the bottom and in the crack.  For mortar, setting times is in hours.
A better way, is to use a concrete epoxy like this. For the epoxy, the setting times may be as short as 15 minutes.  The epoxy is also mixed, but time between mixing and setting up is short. So make sure you have remove all the loose dirt, dust, etc from the stairs and you are ready to apply the epoxy after mixing.
Apply with cheap plastic putty knife.  The epoxy will be thick and heavy.
You might do this in two session.  Do the bottom first to set the piece in place and level.  After the epoxy has dried.  then mix a second batch and apply to the crack on top and side and bottom seam.