The main causes of wobbly steering when driving at low speeds are problems with suspension systems, unbalanced wheels, damaged wheels or damaged tires. Some of the problems indicate a serious issue that should be addressed immediately.
The first thing to check if the steering of a car is wobbly at low speeds is the wheel balance. This is something that most tire replacement shops can handle. If that is not the problem, inspect the wheel for damage. The wheel bearings could also have collapsed.
If there is nothing there, next check the tires. They could have cupping which will look like small waves on the surface of the tire. Or they could have a flat spot which is where part of the tire is flattened instead of round. This sometimes occurs if the tire has been skidded.
The tire could also be separated, which is a serious issue and should be addressed immediately. Note that most problems with tires or wheels are usually consistent. This means they will always occur at particular speeds. If the problem is intermittent the cause could be elsewhere.
Other causes of wobbly steering at low speeds include the steering or suspension system. This could be anything from the steering linkage to the shock absorbers to the ball joints, so the issue would need to be properly diagnosed by a mechanic.