Summary
The more you know about using a telescope and astrophotography, the better.
You will also need access to high-quality telescope with an aperture of approximately 8" or more (smaller aperture might work for a very limited number of targets) and a high-quality astronomical camera.

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Abstract
In astronomy, a transit (or astronomical transit) is a phenomenon when a celestial body passes directly between a larger body and the observer. As viewed from a particular vantage point, the transiting body appears to move across the face of the larger body, covering a small portion of it.The word "transit" refers to cases where the nearer object appears smaller than the more distant object. Cases where the nearer object appears larger and completely hides the more distant object are known as occultations.
The transit method can be used to discover exoplanets. As a planet eclipses/transits its host star it will block a portion of the light from the star. If the planet transits in-between the star and the observer the change in light can be measured to construct a light curve. Light curves are measured with a charged-coupled device. The light curve of a star can disclose several physical characteristics of the planet and star, such as, density. [Source: Wikipedia, https://en.wikipedia.org/wiki/Transit_(astronomy)]

An example line graph shows the magnitude difference over mid-transit time in hours of an exoplanet. Data collected from a telescope shows a dip in light an hour before and after mid-transit of an exoplanet in-front of a star. The largest magnitude difference of the decrease in light is about 0.035 mag at the peak of the mid-transit path of the exoplanet.
Figure 1. Light curve of exoplanet WASP-10 made November 14, 2008, with a 14" Meade LX-200 telescope and no filter, by Bruce L. Gary.
High-quality amateur astronomical equipment can be used to measure an exoplanet light curve. It is extremely unlikely that you could detect an unknown exoplanet by pointing your instruments at a random star; however, it is quite possible to confirm potential exoplanets discovered in surveys such as those produced by the Kepler Space Telescope or the Transiting Exoplanet Survey Satellite (TESS). You might even be able to have your results published. To get started creating your experimental procedure, consult the resources in the Bibliography section.
Bibliography
Search for a PDF of this book on the internet.
- Gary, Bruce L. (2010). Exoplanet Observing for Amateurs, Second Edition (plus), 2010. CreateSpace Independent Publishing Platform.
- Conti, Dennis M. (2018, October). A Practical Guide to Exoplanet Observing, Revision 4.2, October 2018. Retrieved December 16, 2019.
- Poddany S., Brat L., Pejcha O. (2010). Exoplanet Transit Database. Reduction and processing of the photometric data of exoplanet transits (arXiv:0909.2548v1). New Astronomy 15 (2010), pp. 297-301. Retrieved December 16, 2019.

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