How do I exchange one cryptocurrency (not BTC) to another (not BTC)? What if I want to exchange one cryptocurrency (not a Bitcoin) to another (not a Bitcoin). How can I do that? Do I need to exchange it first for a Bitcoin and then exchange a Bitcoin for the target currency?

I know there's something like Changelly or ShapeShift, but what if I want to do it manually, or is what I've described above what these guys do under the hood (that would suck so much)?
Exchanging means you are swapping one currency for another. That means you need to find someone who has the currency you want, who also is willing to swap for the currency you have. The purpose of exchanges is to make that 'finding' process easy, because lots of users meet on an exchange to swap their currencies around. There is no way to 'manually' convert one currency into another without swapping with someone, because each currency is different.