The easiest way to check up on high school football scores, player stats and schedules is to check on teams' individual school websites. For a quicker and less in-depth approach to check scores, MaxPreps is a good place to start.
MaxPreps is a website that not only looks at high school football teams, but also gives scores for baseball, basketball, girl's basketball, volleyball, and many more. If it's a high school sport that has scores, it can be found on this site. Recent activity on a team can be found by searching for the school, then the sport. Some schools have limited information on them, and the site relies on outside contributors to keep the lesser known schools kept updated. You can also check player stats, rosters, pictures and more if you sign up as a member. Membership also gives you access to submit scores or other information about a school game.
However, if a somewhat incomplete website is not top choice, one can also find most, if not all, of player stats, pictures, game information, scheduling, and game scores on each team's high school website. Most local newspapers also often disclose scores of high school games in the area.