You clear it by taking out enough of the larger trees to allow light in and remove all the underbrush. Then you sow grass seed or lay sod- which and when depends on your location.

It can be a daunting task- we have a large portion of woods beyond our "real" lawn/yard. We clear and push it back several feet a year- we use the trees for firewood and compost everything we dig out, then keep it mowed.

You could benefit by having a consult with a reputable arborist. You may not need to remove as many large trees. Depending on the type they may be able to elevate the canopy by removing the lower branches to allow more light to come in the area.