We have inherited poor, rough grazing. Ours is wet and acidic and full of seaves (Juncus rushes).
So - our main tactic is drainage and mowing. Secondary tactics include harrowing, then seeding through with a specialist seed mixture with clover, and liming.
Mowing will help push the species back towards grasses that grow short and harrowing will rake out the moss. If you make 'holes' though, whatever fills them might not be what you want. Here it would be docken or seaves, hence us seeding.
Whether you need to drain, lime or whatever will depend upon the soil as Fron suggests so it would be worth talking to local farmers (who will know) or getting a test done.