When you get off the bus at the port you will go through security. Your carry-ons will be X-rayed and you'll walk through a metal detector. Just like at the airport, being prepared makes things go smoother...you can keep your shoes on here though.
You'll head up the escalator and if you haven't done the cruise check-in at your resort (if you have you'll have your boarding number and KTTWs in hand already) you'll need to get in line to check in. At the desk you'll fill out paperwork saying you haven't been recently sick, get your passports scanned, and you picture taken. They'll give you your KTTW cards and a boarding group number (if you are there early enough).
If you have a boarding number you wait until they call it, if you're there later in the day you'll probably just head right onto the ship. You'll walk through the big ears and up the gangway, getting your KTTW card scanned on your way onto the ship. You'll also get your first professional picture taken (important for the Dream's facial recognition software). They'll announce your entrance onto the ship and everyone will clap for you.
From here, where you go is up to you! You can eat lunch at Cabanas or Enchanted Garden. You can change into swimsuits and jump into the pool. You can explore the ship and wander around until you can get into your stateroom.