What must a person do to fulfill his vow to God to strive in doing good, after God has blessed him with progeny, in addition to being charitable to ten needy people?

A promise to perform an act of obedience is not considered a vow (nadhr) unless it is made with the intention [of it being a vow]; otherwise, it is merely a promise. It is commendable to fulfill a promise as a matter of etiquette with Allah, even if it is not obligatory. If you intended your promise to be a vow, then a vow of striving in good deeds means exerting one's utmost effort therein. The minimum degree of exerting effort has not been specified, but as long as you have qualified your vow with "as much as possible," then be sure to participate in all avenues of good presented to you to fulfill your vow.