How to observe neutrinos? I know that neutrinos are the weakly interacting particles[possibly zero mass] that can pass through matter without any effect which makes them very difficult to detect. But I have heard that they have still been able to capture. I want to know how?
Can an amatuer experimenters like me capture them at home?
 A: The trouble with observing neutrino isn't just getting events (neutrinos are copious and ubiquitous, after all), it's knowing and showing that you have had neutrino events. There are many, many backgrounds to be dealt with and neutrino rates are small so misidentifying even a very small fraction of the backgrounds will swamp your real signal.
There are four mechanism of main interest:


*

*Radio-chemical processes. This was the mechanism of the Homestake Mine experiment. Tricky and indirect so it is mostly of historical interest.

*Inverse beta-decay Actually the reaction that goes by that name is
$$ \bar{\nu} + p \to e^+ + n $$
and it is detected by noting the delayed coincidence between the prompt annihilation of the positron and the subsequent capture of the neutron on a (on gadolinium, boron, chlorine, hydrogen, or carbon). This is the mechanism of the Cowan and Reines experiment and of larger reactor experiments like KamLAND, Daya Bay, and Double Chooz. This has the advantage of few background that mimic the signal, but it requires a DAQ system that can detect the delayed coincidence. 

*Ring-Imaging Cerenkov Usually in water but also in ice. The neutrino interacts to make a charged particle of some kind that then creates Cerenkov light that is detected by an array of detectors that reconstruct the interaction from the light geometry. Again this calls for a fairly sophisticated DAQ, and it has many backgrounds.

*Direct ionization detection (drift chambers, TPCs, solid-state, photographic emulsion) Again the secondary particle from a neutrino interaction are responsible for the signal. The ionization is detected by in a time-projection chamber, by solid-state electrons or even in photographic emulsion. Backgrounds abound.
For very intense sources, say right next to a nuclear reactor, you can get tens to thousands of events per day per ton of detector. For more diffuse sources you may needs tens of tons of detector to get one event per day (or more).
In all cases, going underground to reduce the cosmic ray background is helpful, but you can build a cosmic veto array over the detector to reduce the backgrounds at the cost of some dead-time.
The Cowan and Reines detector was only a few hundred kilograms, and the DAQ was primitive by modern standards, so this is a project that a sufficiently sophisticated hobbyist could attempt, but it will be thousands of dollars.
