To the Calvinist faith is a gift of God otherwise the claim is it is a work of man,
I don't consider myself a Calvinist, just a believer. But I see some problems with your premises.
I think we all can agree that "faith is a gift of God".
and yet it takes a man to put faith to use, so it ends up being a work of man because it is the person's faith not God's and God does not believe for man.
Wrong. It takes God to create a believing mind so His faith could flourish in man and we become His children.
Where do you think belief/faith came from, is it something man or God came up with originally? Here is a link to a 100 Bible verses supporting the claim that God uses belief/faith in order to make Himself known to believers only.
And faith takes a person's will to put it into effect, so man is actively involved in the mental act of the decision to repent and believe.
Not if everything that leads to man's salvation originated in God, including our belief/faith, then salvation is purely a act of God, because everything that makes it occur and possible came from Him to begin with.
How do Calvinist reconcile this obvious issue within their thinking?
God bless
A believer that understands the Bible can explain why they believe salvation is purely an act of God. See above.