How long should you wait to see a response to a remedy?

A general rule of thumb is that a condition should get better in the same amount of time it took to develop, or faster. The more intense and acute the situation, the faster the correct homeopathic remedy should work. It is not uncommon to see changes within a few seconds or minutes in response to a remedy when there is intensity. You may see a fever go down quickly and the eyes look better within minutes, for example.
With some situations such as a flu with a cough that gets worse at night, if you give a remedy during the day, and the cough worsens again at night, it may not mean the remedy was incorrect, because the pattern is one that flares up at that time. Look for improvement over the course of a few days. If you are able to recover from a cough in a few days, where other people with the same flu are suffering for a few weeks from apparently the same illness, a few days is an acceptable time frame. It is not realistic to recover from a cough in a few minutes or hours. (The sooner you take measures to intervene when a cold/cough appears, the better).
For some situations you have to remove a contributing cause. For example, if you take the correct remedy for your carpal tunnel, but continue to do the type of work that led to the condition, and not do the recommened exercises / stretches, the remedy will not have a chance to be effective.
For chronic conditions it would necessarily take more time. Homeopathy, used correctly, should be given at least a month for every year a person has had a condition to see progress, for example with Lyme disease.
Of course, please consult with your licensed medical practitioner when needed.