Turbo overviews       

       
Exhaust enters at the top hole on the right, goes through the turbine blade (not visible), and exits out the end on the right side of the picture.
Air is drawn in through the hole on the left end, compressed by the impeller blade (not visible), and exits the pipe facing away in this picture.

    
Impeller (intake) end.  Air is drawn into the impeller, pressurized by the impeller, and output through the exit pipe on the left.
The exhaust input to the turbo is on the right - it drives the turbine blade on the opposite end of the shaft from the impeller blade.

  
Turbine (exhaust) end.  Exhaust enters from the left side (in this picture), spins the turbine blade at high rpm (100 000 or so), then exits from the end you are looking into.

Turbine (exhaust) end, shown with the wastegate open.  When the wastegate is open, exhaust goes through the bypass port, then directly out the end, to the downpipe; thus, the turbine blade is not pressurized and turbo output pressure is reduced (the wastegate doesn't open this far in reality).