Doing one corner of the vehicle at a time, force one corner of the vehicle to bounce then let go, if the vehicle bounces more than 1 1/2 times after you let go the strut or shock is bad.
struts are a wear and tear item - you can replace one at a time if you mostly drive on the freeway or non performance oriented - if you take your car to the track or drive aggressively around turns...
Some people call it the "Dogbone" mount. Because that is what it resembles. It is located underneath the engine on the passenger side. It prevents the engine from spinning around when you give it gas...