The difference between Ranked and League mode

After having played a few matches:

It seems as though you need the majority (75%+) of the Splat Zone. You definitely do not need anyone in it; I took many from overhead. Taking a Splat Zone means that the whole thing will briefly turn to your ink color, entirely (so if it was, say, 95% your ink, it will now be 100%).

If the zone is currently controlled by the opposing team, when your team covers around 50% of the zone, it will become neutral again so that if either team reaches around 75% coverage, it will fully change (back) to that team's color.

If the control switches from one team to the other, the previous holding team will have time added to their timer so they will have to hold the zone for a longer amount of time if they capture it again. The amount of time added is greater if the current time remaining is low and if the zone was continually held for longer. This extra time is separate from the main score and doesn't count when determining the winner.

All maps have either one or two splat zones. In maps with two zones, control of each zone is the same as usual, but the timer will only count down for a team when that team controls both zones.

In junction to @Vemonus's answer, the wiki adds a bit different wording plus a nice graph.

A Freshness Bonus in Splatoon 2 refers to the proficiency you've earned for each individual weapon. This is different from Judd's coin bonus from the original game.

Each weapon has a freshness rating that will improve every time you win a match. It starts at 0 and goes up one point each time you win a match. Losing a match will subtract from your score, but how much it subtracts depends on your current rating. Once you reach a certain amount, a point bonus is applied.

Take note that while your ranking will continue to go up, the highest you can go is SUPERFRESH! along with all three one time bonuses.