Once you've opened the .cif file and have the correct unit cell and atom positions, click on the 'Boundary...' button at the bottom of the left hand pane. To increase the size of the displayed crystal, change the 'Ranges of fractional coordinates'.
To display only the atoms on a single plane, you'll need to use 'cutoff planes'. First, cut off all the atoms above (further from the origin than) the (111) plane: create a new cutoff plane with indices 1, 1, 1. Set the distance from the origin to be 1 * d, that is, the interplanar spacing of the (111) planes. Make sure the 'Apply symmetry options' box is NOT ticked - we want this operation to apply to one (111) plane, not all {111} planes. Click 'Apply' and you'll see the effect this has.
To remove the atoms BELOW the plane, we need to use a bit of a trick. Create a second cutoff plane with indices -1, -1, -1. Set the distance from the origin to -1 * d. This creates a plane that works in the opposite direction. Click 'Apply' and you should see only the atoms on the (111) plane itself.
Hope that helps,
Philip