Question: How do we discover new planets/stars?

Lewis Wright answered on 13 Mar 2017:

We discover new stars by looking in some direction into space, and holding a telescope there long enough to collect the light that is coming to us from that direction. The longer you collect, the further back in time you are looking.
There is effectively an infinite number of direction to look into space for stars, as even a small angle change over cosmic distances will mean you look into wildly different parts of the sky!

Planet are found by studying the light that we see from other stars and looking for dips in the light.
As a planet passes between us and the star it is orbiting, the intensity of the light we get collect from the star will drop slightly. If we look at the same star for long enough, and we see this same dip happening at regular intervals, then we know there is something orbiting it. From the speed of its orbit, the amount of light that it blocks, and looking at the star it is orbiting, we can estimate the planets mass and size (probably more, but Im not up to date with the latest techniques!)