There were many questions regarding the best option to buy Cardano ADA in this forum, with a lot of the same answers. Therefore I am creating this topic. There are multiple ways to do this. However, I use this process for most of my altcoins.
1. The Wallet
First things first: You will want to have a wallet on your computer to be able to store Cardano. Cardano uses the Daedalus Wallet for that. You can download it here: https://daedaluswallet.io/#download.
You will get an address to send your ADA to in the “Receive” tab. Save that!
2. ETH on Coinbase
No, it is not possible to buy Cardano with your credit card/PayPal. What you will have to do is buy another cryptocurrency and then exchange it to Cardano.
Therefore, create an account on Coinbase.com, (or use my referral link if you want to give us both $10 worth of free bitcoin) where you can use credit card or a SEPA transfer and buy ETHEREUM. You should buy ethereum because it is much faster and cheaper to transfer than Bitcoin.
3. ADA Binance
Next up, create an account on https://www.binance.com/. This is a cryptocurrency exchange which enables you to convert one cryptocurrency into another. It is also one of the few who support ETH > ADA exchange.
Go to your Funds tab after you have registered, where you can find your wallets. Look for the “ETH” wallet and choose the option “Deposit”. You’ll get an address to send your ETH to. Save that one as well.
Switch back to Coinbase and send your ETH to the Binance address - now wait a few minutes.
After 30 confirmations, you’ll have the ETH in your Binance account. Now you can finally go to the “Markets” tab, search for the ETH > ADA exchange and spend all your ETH on ADA. You are now the owner of Cardano!
4. Send ADA to Daedalus
In this last step, you’ll go back to your Deposit/Withdrawal page on Binance, look for your ADA and use the “Withdraw” option to send all your ADA to your Daedalus address. Confirm at least a dozen times that you have copied the right address - if you send it to a wrong one, it will be lost.
This will cost you ~30 ADA - this is normal. Wait a few minutes, and your ADA are now secure in your Daedalus wallet.
Let me know if there are any errors in this. Enjoy your ADA.