Hi. I'm assuming you already have some knowlegde about cryptocurrency, so what you want to understand is on how to acquire altcoins.
First thing you need is to get your very own digital wallet, this is where you will deposit your fiat. Most popular digital wallet that i've read was coinbase, It is base in the US. Depending on your country, there are local digital wallets that you can use. Some digital wallets already offers altcoins, but the only problem is there are only a handful to choose from.
Next thing you need is to find is an exchange. Every exchange has a certain variety of altcoins, so it is important that before choosing an exchange you first need to choose on what altcoins you are going to get. To name a few popular exchange that i could recommend is binance, poloniex, bittrex and kraken.
Lastly is how you can get the altcoin you wish to have. Now that you have a digital wallet, already deposit your fiat, altcoin that you want and an exchange, you can now buy an altcoin. In the exchange just find the deposit section, here you'll need to enter your digital wallet address. Then enter the amount you like to deposit. Im assumming that your fiat is already converted to bitcoin or whatever cryptocurrency that the exchange is accepting. Next is to find the altcoin you want to get. Click on the altcoin, then click buy, enter the amount you want depending on how much you deposit and there you have it, you now have the altcoin that you want.
If you what more detailed instruction on how to acquire altcoins, you can always find it on the internet.
Hope this helps.