The main way of detecting planets is to watch the star over time. When the star pulls planets towards it, the planets also pull the star. Because the planets weigh so little compared to the sun it’s not a huge effect. But it’s there, and minute, cyclical wiggle is a good way of detecting exoplanets.
As for size and distance, that’s a little more technical. But in general distance can be understood by its brightness and the redshift of the star. If you need a more powerful telescope to see it, and if it’s more redshifted, it’s likely farther away.
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