Talk to Nearly Headless Nick at dinner. Have him let slip to the Bloody Baron that you and your friends will be trying to visit Hagrid after dinner. The Bloody Baron will, of course, inform Professor Snape of your plans.
Walk across the grounds toward Hagrid's cottage, making sure that none of the teachers see you leaving. When you are almost to Hagrid's, crouch down under your invisibility cloak, making sure that no part of you can be seen.
Use the Marauder's Map to find out where Snape is. When the map indicates that Snape has left the building, prepare your wands.
Use your wand to cast the Petrificus Totalis spell on Snape as soon as he is within range. As a bit of insurance, have one of your friends case the Expelliarmis spell on him, as well. This will result in Snape being totally paralyzed, with his wand flying away from him and out of reach.
Cast a Silencio spell on Snape next, ensuring that he will make no noise to attract anyone to assist him. When casting Silencio, make sure that you give the wand a sharp jab, not a wave.
Cast the Locomotor Snape spell loudly and clearly. This will allow you to walk to the Quidditch grounds, with Snape floating along behind you. When you get to the Quidditch grounds, place Snape at the base of one of the flag poles.
Silently cast the Levicorus spell. This will result in Snape being hung in the air by one ankle. As soon as Snape is in the air, use Accio Broom to bring your Firebolt to you.
Ride your Firebolt to the top of the flag pole, and grab Snape's ankle. Securely tie Snape to the flag pole rope.
Cast an Obliviate charm to totally erase Severus Snape's memory of this entire incident. Ride your Firebolt down to the Quidditch grounds and join your friends.
Walk away from the Quidditch grounds and move on to the Shrieking Shack to do your investigative work. Make sure to use the Obliteration Charm to get rid of any tracks that you may have left in the grass or dew.
Hide under your Invisibility Cloak when returning to Hogwarts to ensure that no one observes your passage.
Go to the library and sit in a quiet corner. Allow Madam Pince, the librarian, to notice you once you have the table covered in books. Complain about being there all night doing homework so that she can hear you. This will be your alibi.