Foundation problems are inspected with leveling tools that are very sensitive such as this ZipLevel. The main unit would be placed in the center of the building and then measurements are taken in each corner and in other key places and plotted on a drawing of the building. Once all measurements are done, some math can show you the inclination of the foundation, and problems like tilting or cracking become appearant.
That device retails for around $700, but for a cheap, do-it-yourself option, a simple water level can be used. You can look up water levels, but at its most basic, its just a clear tube filled with water that is open on both ends. You hold the ends of the tube up and the water on both ends will be level. You measure from the floor to the water level and by taking several measurements, you can see if the foundation is tilting.
If the foundation is tilting, remediation is a bit beyond DIY. Catching the problem early is best. A root cause also has to be determined so future problems can be prevented. Poor drainage and even plumbing leaks can be major contributors.