Make the layout of the page. You will need the header to hold "You" and "Computer," divs for where the player's and computer's choices show up, and a place to notify the player who won. Feel free to be creative with the layout and design it however you like.
Find pictures for rock, paper, and scissors and format them on the page.
Make the objects (the rock, paper, and scissors) draggable. Make the div that is supposed to hold the player's choice able to receive a picture if it's "dropped" there.
When the object is dropped, figure out how to make the computer recognize which picture it was. (This will be important when you're trying to determine who won.)
Have the computer pick a random number between 1 and 3. Assign the numbers to rock, paper, and scissors.
When the object is dropped, tell the player somehow if they won, lost, or tied.
Add two fists (one for the player and one for the computer) that show up when the weapon is dropped, and then have a countdown (rock, paper, scissors, shoot!) before the player is alerted of who won
After "shoot" have your chosen weapon show up and have the computer's show up based on the number between 1 and 3
Animate the hand so that it moves up and down during the countdown
Once the winner is decided, have the game automatically restart
Keep working on your game until you're happy with it. Add fun pictures to tell the player who won, find a cool font using Google Fonts, make the computer "think" while you're choosing your weapon, etc.