For adding your new project to Github you need github account. If you do not have one you can create one by visiting GitHub.
Step 1: Right click on your project and go to Team -> Share Project
Step 2: Click on Create Next to Repository dropdown.
Step 3: Enter your repository name and Click Finish.
Step 4: Right click again on your project and go to Team -> Commit
Step 5: Add all unstaged files to stage
Step 6: Enter Commit Message and click on Commit and Push
Step 7: Open Github.com and Click on New on left hand side
Step 8: Enter Repository Name
Step 9: Select public/private and Click on Create Repository
Step 10: Copy URI
Step 11: Navigate to Eclipse and Paste URI
Step 12: Enter Username and Password in Secure Store [it will ask for some information enter information which you can remember]
Step 13: Click Next -> Next and Then Finish -> Close
Step 14: Navigate to GitHub you can see the code in your repository.