1. Check CoinMarketCap to see where you can buy ICON and with which currencies
For each cryptocurrency, CoinMarketCap provides a list of purchasing options (also known as market pairs). Go to CoinMarketCap and search for ICON. Tap on the button labeled “Market” near the price chart. In this view, you will see a complete list of places you can purchase ICON as well as the currencies you can use to obtain it. Under “Pairs” you'll see the shorthand for ICON, ICX, plus a second currency. The second currency is what you can use to purchase ICON. If you'd like to purchase ICX with the U.S. Dollar, look for ICX/USD.
2. Pick a platform to make your purchase
Different platforms have different levels of security, reliability, and liquidity. Before creating an account, do your research.
3. Make the purchase on your chosen platform
Every platform has a different way of doing things. Some platforms are very easy to use, others not so much.
Generally speaking, purchasing crypto with a fiat currency like the U.S. Dollar will be easier than purchasing it with another crypto.
If you do have to purchase ICON with another crypto, you’ll need to first create a crypto wallet that supports ICON, then you’ll buy the first currency and use it to buy ICON on the platform you chose.
If you get stuck, most platforms provide guides. But if they don’t, there is a vibrant community of crypto enthusiasts that have likely posted guides on Youtube, Twitter, and elsewhere.