With 8 days, you'll be able to see Rome at a relaxed pace.
One of your first steps is to get a guidebook and familiarize yourself with where the various sights are located relative your hotel (and you'll get better advice if you mention the name and address of the hotel).
Given a reasonably central hotel, nearly everything you'll want to see is within walking distance or a short bus ride. But take your time - you have a relatively long stay so you can work with one destination per day and not kill yourself rushing around. For example, St. Peter's Basilica & Vatican Museums would cover a good chunk of one day (and be fairly exhausting), then another day for the Colosseum/Forum/Palatine, etc.
To fill in time between the major sights be sure to stop for a cafe and a pastry, some gelato, etc. And be sure to stop and enjoy the smaller churches - many have remarkable histories and interiors that will amaze you.
Finally, for many basic answers, be sure to browse the links right over there ->