Question

What methods are used to detect planets around distant stars?

Answer 1

Direct observation
Transit method mostly by Kepler space telescope.
Wobbling action of star when planet comes near to ,it in orbit. Doppler spectroscopy).
gravitational lensing.

Explanation:

Only very few planets were observed by this method.
Majority of Exo planets were detected b y this method (Transit). by Kepler space telescope.
Picture credit Mission backup earth.com.