The second way is adding it to your native Mail application. It may seem simple to add it as you would add any other email account. Problem is you don't get your email pushed to you when you set it up, read on and I will let you in on the trick of getting your Gmail account to behave like the rest of your mail accounts.
The trick is setting up your Gmail as an Exchange account rather than a Gmail account.
Go to Settings>Mail,Contacts, Calenders.
If you have added a Gmail account already delete it here by selecting it and pressing the Delete Account button at the bottom of that screen. (Don't worry this wont delete your emails or anything like that)
At the bottom of the account list press Add Account...
On this screen select Microsoft Exchange instead of Gmail.
Fill out the screen with your email address, leave domain blank, username (the part of your email before the @ symbol) your Gmail password and Description (The Description is what ever you like it to be, it's how your Gmail account will be named in the Mail app of your device) Once you fill this screen out click next.
You will get Verifying than another screen that shows all the same stuff you filled out and adds a new line called Server enter m.google.com there, press next and you are good to go.
Your Gmail will now be added to your Mail App. When you get an email it will be pushed to your phone, you no longer need to go to your mail and manually check for new Gmails.