Go to the 2-Step Verification page. You may be required to sign in to your Google Account. Click the Get Started button.
You will need to verify the account that you are enabling 2-Step Authentication on.
Enter in your phone number including the area code. If your number is an international one you will need to change the country by clicking the icon near the America Flag displayed in the following screenshot. You will be given the options to have codes sent via text message or via phone call, select the button next to your preferred method. Click the Send button.
Depending on which method you selected in the previous step you will either receive a text message, or a phone call. You will be provided with a 6 digit verification code. Enter the code in area provided. Click the Next button.
If you did not receive a call or text containing the verification code click the Resend button. A new verification code will be sent. Please keep in mind that it may take a few moments for the message to arrive, if you request a new code, and both codes come in at a similar time, the newest code will be the correct one to use.
Once the verification code has been entered, you will be asked to turn on 2-Step Verification. Click the button Turn On to enable it.
Once 2-Step Verification is turned on you will be brought to a page where you can manage your devices and phone numbers. If you wish to change your phone number or remove it, click the pencil icon to the right of the phone.
There are several alternative 2-step verification options available for your use.
Use those links to learn how to setup and use the alternative 2-step verification methods.