What is the best and cheapest way to Exchange cryptocurency?
Without all most 0 fees!!
If you talk about trading fees, I recommend you to use Vindax. It has a fee of only 0.05%, this is the lowest I've ever seen. But besides that, its volume won't be too high, that's the only weakness.
If you talk about fee withdraw, you should use Exmarket. That exchange never charges withdraw. I tried withdrawing 2 ETH and I didn't pay a dime.