First thing first - zakat is calculated yearly on your savings not on your income. As you have no savings to speak of, there is no zakat obligatory to you.
Zakat is from wealth you can spare, its not suppose to put you in debt. That's why its calculated only on savings (not on income) and on ones possessions that are not of utility. For example, if your wife has jewelry that she is wearing daily; there is no zakat obligatory on this.
If she has jewelry stored away that she never uses, then (assuming its of significant amount), zakat is obligatory here.
The zakat that we commonly speak of is one that is calculated at the end of the year (again, from savings) and then is usually put into a fund or deposited to some charitable organization or in some cases distributed by the person directly - and this amount cannot be given to one's own parents, grandparents, children, grandchildren, or spouses (because their care and well being is obligatory on you).
In the Quran there is no "percentage" given, but it is generally accepted that 2.5% is paid on capital assets. There are various other percentages given on agriculture, livestock, precious metals and minerals.
People eligible for zakat include any of the following - be they muslim or not:
- Those living in absolute poverty (Al-Fuqarā').
- Those restrained because they cannot meet their basic needs (Al-Masākīn).
- The zakat collectors themselves (Al-Āmilīna 'Alaihā).
- Non-Muslims who are sympathetic to Islam or wish to convert to Islam (Al-Mu'allafatu Qulūbuhum).
- People whom one is attempting to free from slavery or bondage. Also includes paying ransom or blood money (Diyya). (Fir-Riqāb)
- Those who have incurred overwhelming debts while attempting to satisfy their basic needs (Al-Ghārimīn).
- Those working in God's way (Fī Sabīlillāh).
- Children of the street / Travellers (Ibnus-Sabīl).