zero cost collar means that the premiums of  a purchased put and a written call are very close (not necessary equal), so the cost of the collar will be close to zero.

for a call option, in the money means current share price > strike price, also means if option is exercised, there will be a positive payoff; so out of money means strike price > current share price, if going exercise, would be a negtive payoff.

for a put option, just reverse, in the money, means strike price > current stock price, exercises at a positive pay off; so reverse the out of money comparing the call option too.

at the money means, payoff close to "0"; as you asked, buy a at-money put & sell out-of-money call:
so, the put exercises, payoff = 0; and since "out of money call, premium" will be close to "the premium of a put at lower strike price", so the cost would be close to "0". total profit will be 0.

normally, at time 0, the stock price is not a concern, otherwise there will be the arbitrage opportunities. the put-call parity decides the lower strike premium which is normally the puchased put premium.

hope it helps.

In your example, if the underlying asset's price is 50:
at the money put option: strike price= 50,
out of the money call option: strike price = any price> 50 (i.e. 61, 50.5, 70, etc.)

zero-collar??  I don't know what it is.  Do you mean Zero Cost Collar?  If yes, it simply means the price of out-of-money call option perfectly offset the price of at-the-money put option.

wow ~just like above said~i've nothing to add on

well you do have good comments to add, such as an example, am i right?

i did not give one, leave it to sb. else, you may try ........ and we all share the bonus