Go to the "Git Repositories" view, open the tree of the repository you want, right-click on "Remotes" and select "Create Remote". Remote name is the alias, and the url is specified in the second step of the wizard.
If you have no local branch, there is nothing you can push. You have to create a branch and do one or more commits to push that commits.
Pushing is possible when you right-click on a project or on a repository in the repositories view.
If you commit a change, the branch "master" will automatically be created. Then you can create a new branch, if you right click on the repository, and then choose "Switch to" -> "New branch".
Since branches are pointers to a commit in Git, you must have at least one commit, otherwise there is nothing a branch could point to.