Step 1: Use your computer's browser to login to Coinbase at https://www.coinbase.com
Step 2: Signup for an account with your email address. Use your smart phone to verify your registration code during the process.
Step 3: You will need to provide your Driver license's front side and reverse side as well as your face image via your computer's web camera to verify your identity documents. The process may take several minutes.
Step 4: Add your bank account or credit card or paypal account to your newly created coinbase account so that you can fund your purchases at Coinbase.
Step 5: Optionally (but highly recommended), enable MFA (multi-factor authentication) for your account. For this you will need to download Google Authenticator app in your smart phone first. Then follow the steps in Coinbase to scan barcode after writing down the 16 digit code. This is to make sure if you loose the mobile, you can recover your account access.
Step 6: You are ready now to buy and cell any of those 3 - Bitcoin, Ethereum, Litecoin. Select the respective wallet to buy those coins.
Coinbase charges 4% transaction fee for each purchase. To avoid this fee, you can use GDAX exchange (owned by the same company as Coinbase) for coin trades using your Coinbase account credentials. But this will involve a few extra steps which are explained in detail at http://bitguru.co.uk/how-to-avoid-coinbase-fees/. I will give the gyst or summary of the steps here.
Step 1: Login to Coinbase and add fund to your USD wallet. For example, if you want to buy 2000 USD worth of bitcoin, then transfer $2000 from your bank account to your USD wallet of Coinbase. This may take 3 to 5 business days.
Step 2: Sign up for GDAX at https://www.gdax.com using your coinbase account.
Step 3: Go to top right menu option Trade and click on Deposit button in the left.
Step 4: This should show you the options for Deposit Funds. Pick the option Coinbase Account and transfer money from Coinbase to GDAX.
Step 5: Once the transfer is done (usually instantly), you can now use this money to place a Buy Order from GDAX.
Step 6: You can either do a regular market price buy order or limit price order. If you place market order, you will be charged a small transaction fee of 0.3%. However, if you use limit order then you won't be charged any fee at all.
Step 7: While picking what limit price you should choose for your coin to buy, pick a price same or very close to the top price (green color) of the lower half frame to make sure your order gets processed right away.