It boils down to sheep, cattle and manual labour.
This website gives a good introduction and some links to "estate keeping" in Great Britain at Jane Austen's time. Let me extract the major points:
First, you need to distinguish between the larger fields / meadows further away from the house and the adjacent grounds.
Lawn care (or, perhaps "meadow care") relied much on sheep and cows and sometimes deer who would keep the grass short by grazing and fertilize at the same time. As visible fences were considered "ugly" - the goal was to create a "natural" landscape even though sometimes major changes were made like transplanting mature trees or creating artificial lakes - a ha-ha kept animals from freely wandering onto the lawns near the house. Assume that these meadows appeared less evenly than if mowed by a tractor, but that's not crucial if viewed from a distance. To even out, they could be mowed down manually with a scythe. This required many labourors.
The grounds closer to the house could be "mowed by sheep or cows", too. Remember that the owners would not necessarily be in residence all the time. Assume that most of the droppings would be removed by the gardeners. But mainly the upkeep was done by hand (scythe), the source claims cutting once a week in the morning and flattening the grass with a heavy roller would ensure an even, short lawn that even the ladies with their dainty shoes could comfortably use.
As for watering, I'm quite sure that the gardeners would rely on the wet English summers...