Scarification is a good start.. this will help get any loose moss out of the lawn as well as grass or other bits and pieces. You could then use a variety of chemicals, but i'm not really for those.. I prefer a natural approach.
When it comes to moss, it can be tricky. A weed and feed will be a good next step.
Make sure your lawn receives enough light and not too much water.
Moss thrives in dark moist conditions.
Aeration and then laying more grass seed is a good annual lawn care 'tip'.