What is the method of giving Zakat?
"If you give alms openly, it is well, and if you hide it and give it to the poor, it is better for you; and this will do away with some of your evil deeds; and Allah is aware of what you do." [Al-Quran 2:271]
It is obligatory to make an intention for the fulfillment of Zakat, just like it is obligatory to make an intention for Salah. Further, it is not necessary to reveal to the needy person (to whom Zakat is given) that the cash or kind which is being given to him is Zakat. If one gives a deserving person some money as a gift, but makes the niyyah of Zakat, it will be valid.
Zakat will only be valid if the recipient is made the owner of that amount. Zakat cannot be given or used for the construction of a masjid, madrassah, hospital, a well, a bridge or any other public amenity. Authority can be delegated to another person or an organization for the distribution of Zakat so that it can be utilized in accordance with the laws of Zakat. If an agent is given Zakat for distribution, and he does not distribute it, then the Zakat will not be regarded as fulfilled, and the sin of not discharging the obligatory duty of Zakat will remain a burden on whom it was obligatory.
For an example case study of Zakat calculation, please see section "How to Calculate Zakat"