Score entry can be accessed from a league's main page. You can get to any league's main page by clicking Leagues on the menu:
Then click the Fixtures button on the relevant league. You may need to select a different playing season to find the league.
Scrolling down this page, all rounds are available.
The Go to round buttons make it easier to jump to later rounds:
The Enter scores for round button accesses the score entry page:
Type in the numbers and use the Tab key on the keyboard to quickly jump to the next field. Alternatively click on each field as you go along.
When all scores are entered, click the Save button.
The scores are saved and the table is updated immediately.