Check the roof to survey the extent of the damage. Trees can seriously compromise the structural integrity of the roof, so assess whether you can safely climb on the roof to perform repairs. Use a ladder that's at least 2 feet taller than the roof line so your ladder will still touch the roof line if the ladder slides. This will keep the ladder from toppling over. If necessary, have someone hold the ladder to keep it from falling or slipping. Never climb on wet, slippery roofs. Wear shoes with good treads, and walk along the nail lines.
The tree's impact might simply have broken some shingles, which you will need to replace after having the tree removed. You can inspect cracked rafters or a bowing roof sheathing from the attic. A tree can pierce the roof if the wind propels a branch at a great enough velocity.
Besides the damage caused by the impact, any rain occurring after the damage will cause water damage and can also cause long-term mold and mildew problems in your home. You can use tarps to minimize the water damage by covering up the hole in the roof and by placing the tarp on the floor of the attic. Damage can also lead to clogs in the gutter system, which can cause the basement to flood due to improper drainage. You might need emergency roof repairs to limit the extent of the damage.
Emergency measures will keep the roof sealed until you can hire a contractor to perform roof repairs. Plastic roof cement works the best on damp surfaces. Avoid using liquid products, as they hinder a contractor's ability to find the leak. Sealant and roof tape work well on smooth roof surfaces. Do not perform these repairs during a storm.
If you have insurance, document the extent of the damage and photograph the damage and fallen tree so you can make claims and recover compensation. An adjuster may come to assess the damage. The insurance company should cover both the costs of removing the tree and the costs of repairs.