Since the invention of the car, one of engineering's greatest challenges has been to build a car that possesses both a smooth ride and sharp handling. Solid axles that transmitted bumps across both sides of a vehicle were gradually phased out and replaced with semi-independent or fully independent suspensions. An early type of theses suspensions is the trailing arm design. This large arm allowed independent movement of the wheels. The semi type has the arms inclined to a certain degree. Compared to a swing axle, these are much more stable and provide neutral handling.
A trailing arm rear suspension was very common in the 1970s and 1980s. BMW, Porsche, and Mercedes all used them on some cars. They were largely replaced by double wishbone and multilink suspensions on most cars. They are usually made of heavy metal and they can become rusty or broken. When this happens it may become difficult to control the car. This could be a simple wandering feeling in the line of the car or could be complete loss of control. In addition to the difficult handling, you may also experience sever tire wear with bad trailing arms.
Replacing a trailing arm is a complex job. It may be that you only need to replace the bushings on the arm. Here are some basic, general instructions to give you an idea on what to expect but they are not a substitute for speaking with a qualified mechanic. Make sure that you have all the correct parts or tools. Have plenty of light.