There are a few websites where you can start taking your first steps:
1. Coinspot
2. Independent Reserve
3. Coinbase
4. ACX.io
5. BTCMarkets
6. Coinjar
Once you have put money into these exchanges people typically purchase one of the three main crypto currencies (BTC, ETH or LTC) which are then used to purchase other coins (typically on larger exchanges because of lower transaction fees)
The major exchanges are:
Binance
binance.com
KuCoin
https://www.kucoin.com
Bittrex
https://bittrex.com
Just have a look around and choose which one you like.
Hope you have fun!