All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
You are not obliged to pay Zakaah on your monthly salary if it is less than the Nisaab (minimum amount of property liable for Zakaah, that is 85 grams of pure gold or its equivalent). If it reaches the Nisaab and one lunar year has passed over it and it remained unused or unconsumed, then you have to pay Zakaah on it. The amount of Zakaah you have to pay is 2.5 percent of your whole wealth.
If one saves something from his salary and it reaches the Nisaab, after completing the Nisaab if a lunar year has passed on that amount then he has to pay Zakaah on it. If the amount of Nisaab reduces during the year and he regains it, then he can resume the year for paying Zakaah from the time of regaining the Nisaab. You are obligated to pay the Zakaah of your wealth since you are the owner of that money. Your wife is not required to pay Zakaah on the share you give her. But if she has her separate sources of income, such as salary or whatever, then she has to pay Zakaah with the two conditions mentioned above.
Allah knows best.