There is Systemic, which allows anyone to browse through radial velocity data and detect planets. Fits to the data may be uploaded to the "backend".
http://oklo.org/downloadable-console/Tutorial 1Tutorial 2Tutorial 3This requires no equipment of special knowledge (aside from how to work the programme of course, which are what the tutorials are for).
If you have a telescope (preferably with an objective diameter above 5 in or so) and a CCD (charged coupled device, they measure light intensity, they're in your scanners, digital cameras, etc), then you can detect a few of the bright transiting planets (HD 209458 b, HD 189733 b are examples). The better the telescope, the more you can detect.
Here's a pdf that deals with detect transiting planets for ametures.
http://brucegary.net/book_EOA/EOA.pdf
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