Even we see giant stars as tiny points, how can we discover planets that are small and with no light? Suppose you are observing the sky with a strong telescope. Because you don’t know exactly where you need to look, you focus on stars. If you’re lucky enough you can notice a slight variation in brightness as a planet passes in front of the star. And then you have to wait to see the same. This might be 1 week, 1 year or more. It depends on how long will it take the planet orbit the star.
When you see that variation in brightness again, you can calculate how much time passed between the first and the second. Now you wait to see that effect exactly at the end of that time. And ultimately, if this happens again at the end of your calculation, congratulations, you’ve discovered a new planet!
This method is called transit method and the most successful way of finding planets. But wait a minute! Have you noticed that you have never seen the planet you’ve been exploring for so long? Yes, you actually discovered its shadow.
The first planet beyond our solar system was discovered in 1991 with a similar method. Until that time we only assumed that there are planets out there. Today we know thousands of them in a wide variety of sizes.