Step 1: Create an account on an exchange website. BTCmarkets.net literally took me 20mins to get verified which is much simpler than most other websites. You can then deposit money via Bpay (takes 1-2 days) and once its has gone through you can purchase crypto. BTCmarkets offers ETH, BTC, LTE and XRP. Independent Reserve and Coinbase are alternative to BTCmarkets.
From here you can store your crypto in a wallet. If you want to trade in more cryptocurrencies (altcoins) then you will need an account on another exchange website i.e. proceed to step 2.
Step 2: I created an account on Kucoin ( https://www.kucoin.com/#/?r=1575h ) and registered with Google 2 step authenticator (no ID verification needed as you won't be trading fiat). Other websites such as binance or cryptopia are similar to Kucion, but I find Kucoin to be the best with fees.
Step 3: Withdraw the ETH or BTC you purchased from the first site (e.g. BTCmarkets) and send it to your Kucoin account (I suggest using ETH as it generally has lower fees). You can find your ETH wallet address by clicking deposit button next to the Ethereum option in the assets tab.
Step 4: Once your ETH or BTC has been transferred to your Kucoin account, search in the Markets tab for a currency you have researched and put in a buy request for either the current lowest sell price (this will be an instant buy) or set your own price and wait for the market price to drop.
Step 5: Continue your research and make sure you secure your coins in a wallet.