The most obvious sign that your septic is in need of repair is sewage backing up in you house or your backyard. There are a variety of reasons that a septic tank fails, and there are some costly decisions to be made depending on what went wrong.
If you find sewage in your home, then the water level of your tank needs to be checked immediately. The tank may need to be pumped if the level is too high. However, if the drainfield is saturated, which can be caused by flooding, then you need to wait before pumping. Drainfield failure (not from flooding) can quickly become a biohazard; as such, you need to get children and pets away from standing water or soggy soil. Time can cause drainfield problems, as well as not pumping frequently enough, or allowing grease and solids to build up to unsustainable levels and get washed into the leach field.
When and how to repair the problem is easily based on what has to be done. If it is just a broken pipe or crushed lines, then it might just be a few thousand dollars. However, if a drainfield has failed, then you will likely need to repair or replace the system.
Regardless of the repair specifics, you should always consult a professional service provider that can advise you on the required procedures involved in replacing (or repairing) a system.