Gmail is the email system that Google has and has been around a number of years. Accounts are free with GMail.
To get a g-mail account go to gmail.com The account you create here will work for any of the Google applications including Google, Gmail, BlogSpot, Google+ and others. If an account appears that is yours you can just login thru it to create a Gmail account. If the account that appears is not yours choose Sign in with another account and then choose add account, then Create an account. If no account appears choose Create an account.
Enter the information requested such as your name. You will also choose an account name that will be your email address combined with @gmail.com Choose the name carefully (Google will tell you if the one you chose is already in use and have you choose another) as this name will be what appears to people when they email you. I have seen email addresses that made a bad image of a person. I tend to choose email addresses for myself that use my name and possibly a number. My Gmail account is firstname.lastname@example.org
It asks for your cell number and another email address. These are useful to getting the password back if you forget the password or your account gets hacked and password needs changing back after they changed it. Google will not use them for other purposes is my experience.
There is a check box to change your homepage in your browser to Google. Unless you want it changed to Google (what you see when you start browser such as Internet Explorer or Firefox or Chrome) uncheck the box
At the bottom you have to type in a capcha code you see on the screen. This is to keep machines from creating lots of email addresses that are then used maliciously. Then click the Next step button
It will then ask about creating a profile for Google+ which is Google’s social media application. You can choose No thanks or you can set up profile (you can do profile later also).
You have successfully set up your email address. With a Gmail address you will be able to keep the same email address no matter what ISP (Internet Service Provider) you use.