Make sure you watch your flights. When you booked, you were given a confirmation code. Go to Delta's website and enter that code to make sure they haven't changed your flight times, seat assignments, etc. Do this every day since you are leaving soon.
Then 24 hours before your flight time, go to the Delta website and check in for your flight. You will have to indicate how many bags you are checking. If you pay for them in advance it is a little cheaper. Print out your boarding passes. Don't wait to check in at the airport on the day of your flight. If they have oversold your flight, you could be placed on standby or be bumped. I have read that this is sometimes done based on the last passengers who check in.
For your return flight, you need to check in online again and print your boarding passes for the return flight.
When you get to the airport: If you are checking bags you need to go to the counter to give them your bags. If you are only using carry-on bags, you can go straight to the security checkpoint with your boarding pass.
Since you haven't flown in a while, make sure to read about what can/can't be in your carry-on. Delta's website will give the specifics, but basically anything in liguid/gel form that in in your carryon bag must be in containers that are 3.4 (?) oz or less and all of those containers must fit within one quart-sized ziplock bag. Each passenger is allowed one ziplock bag. This bag must be removed from your carryon and placed in the plastic bin at security.
You cannot bring drinks with you on the plane unless they are purchased past the security checkpoint. To get around this rule, you can bring an empty water bottle and fill it at a water fountain past security. We bring individual lemonade packets to add for flavoring. You can bring any food you want, as long as you don't bring things that are in a gel (like pudding, jello, jar of peanut butter). We have found this to be really helpful when traveling with kids, since drinks and snacks never seem to come fast enough on a plane!