The first is mining and for the most part this is going to be a waste of time as it takes so long to mine just one coin and depending on coin type may take some very high priced equipment to even get started.
The second is selling items and accepting payment in one of the coin types. This does work although there are still not that many people who want to pay that way.
The third way is to use faucets. There are many types of faucets and you can earn while playing games, donating computer time, or doing any number of other tasks.
There are literally hundreds of websites that you can go to and get coins of different types while just having fun.
You also will need to have a wallet to store your coins in. You can get one for free. Just search for your coins name and add wallet to the end and you can find plenty of free places to go to. Be sure and check the security.
I do not think you will get rich by doing this but you can pick up some extra cash. This is really good for low paid people.
Right now one Bitcoin is $200+ and the other coins are all different values.