Firstly determine the repairs you need to make. Essentially, these can be categorized into minor or major repairs. Minor repairs will reflect on the house's habitability assessment. These assessments may not be a part of the actual contract but will be regulated by the law, where it is a landlord’s responsibility to carry out all minor repairs. The same goes for major repairs which may include broken furnaces, doors, or deteriorating overall condition of the home.
With regards to any claims, it is essential that you do your home work first. This will include knowing all regulations and laws in your state, reviewing your contract agreements or the advertisement which prompted you to choose this location at the first place. All will have certain fine prints which will work in your favour.
Also, it is your duty to show that the damage was not your fault. It should not be caused by any of your guests, or be a result of your own carelessness. At this moment, you must take pictures of your house in order to build your case. You most likely would have taken some when you rented it, so get the information sorted out.
Now is the time to contact the landlord. Ideally, you would want the landlord to make immediate repairs if the issue is serious or needs urgent attention. However, if the landlord refuses, having all the relevant information will be very useful for you.
Call the local state health inspector, or any another legal person to help you out. Provide him or her the information you have collected and more often than not, you will be compensated.
Most tenants use the repair-and-deduct-option where they deduct the cost of the repairs from the monthly rent. However, exercise this option only as the last resort or if the repairs needed immediate attention, as most states will hold you liable for holding the monthly rent.