Exchange with / exchange for
I'm a little confused with the usage of "exchange with" and "exchange for". Do they have the same meaning? If not then how do you use each of them in what occasion?

Also is "You should exchange your (recently bought wrong sized) shoes with different size shoes" correct?

Question

Exchange with / exchange for
I'm a little confused with the usage of "exchange with" and "exchange for". Do they have the same meaning? If not then how do you use each of them in what occasion?

Also is "You should exchange your (recently bought wrong sized) shoes with different size shoes" correct?

Answer

I think that it works like this: You exchange one thing for another thing. You exchange things with someone.
So - 'I need to exchange phone numbers with her'. 
And in your example 'exchange one pair of shoes for another'.

Answer

Gary is correct. Exchange with is for the person who you make the exchange with. Exchange for is the items you exchange.