How to find Exomoons? How would we be able to detect Exomoons? We detect exoplanets by seeing if the light gets faint from a star, but could we really use the same method for determining if there is an exomoon around that exoplanet? Thanks for your thoughts and answers!
I'm going to try to take a stab at answering this. With our current technologies, detecting exomoons can prove hard however there are various techniques being used today such as:


Analyzing data from the Kepler Spacecraft
Dynamic effects – the exomoon tugs the planet, which causes deviations in the times and durations of the host planet’s transits. This is similar to the radial velocity technique for detecting exoplanets. Source: UniverseToday
Transit effects – the exomoon may transit the star immediately before or just after the planet does. This will cause an added dip in the observed light. See this video for a great demonstration. This is similar to the light curve technique for detecting exoplanets. Source: UniverseToday
Gravitational Microlensing - which is a technique used to detect exoplanets like you stated above however it may also reveal signs of an exomoon. Read this source


I found this information doing some simple googling, feel free to edit or add to.