You really can't. Mother Nature can't grow grass in shade but has ferns or other forbes. If you can't thin out the trees then look to see what naturally grows in similar areas and plant those. Often that's a far more interesting garden.
maybe you don't need grass there, maybe you could use a vine or green plants like the snake plant that has just green leaves. If you had grass you've have to cut it there and might hit your lawnmower on the roots of the tree. There is, however, grass that can be grown in shady areas. Ask Home Depot or your local tree nursery about that.
Go to your local garden centre and ask them about grasses that grow in high shade areas. Either that or forget the grass altogether and get some shade loving plants.