In order to enter scores, you will need to publish your schedule.
You will see score input boxes on each game starting the day it is scheduled (see screenshot).
Simply input the scores and hit Save Scores on the bottom right.
Standings will update automatically (refresh the page).
Sub Scores / Sets / Games
You can enable subscores (aka sets or games, depending on your sport) via custom standings by turning on the 'track sets' toggle.
You can then reveal the sub-score inputs for each game by clicking the + next to the match score inputs:
Once a match has a score, you can clear that score in its edit game dialog (click the little green icon above the team on the right).
in the edit game dialog, submit empty scores and 0 points (or leave points untouched – those just can't be blank):
Once a score is recorded, you can also change the points given to each team via the edit game dialog (for sports where points are a factor in standings, e.g. soccer, hockey).
The PRO/Tournament version allows you to designate other users as score keepers and enter results: see this article.