There are hundreds of thousands of users without any edits. It is widely accepted (but not required!) that users with no edits should not be welcomed to save on server resources and also because most templates start with "Thank you for your Contributions" (or similar). Furthermore, until edits are made, it's impossible to determine if the user has bad intentions, and created the account purposely to vandalize
Wikipedia.
Check your watchlist – welcome the users who are working on the things you yourself are interested in. The new users are the ones with a red talk page link.
Check Wikipedia's account creation log – this is especially useful with a quick link to their talk page, as well as an "at-a-glance" sign to tell if they've probably been welcomed already: their talk page isn't red linked!
Special:ActiveUsers – a list of users who had some kind of activity within the last 30 days.
You will no doubt come across new users as you work on Wikipedia. You may spot them in the edit histories of pages or on talk pages. If a user's signature or username is in red, that indicates that they don't have a user page set up yet. That means they are very likely (but not always) a new user. Check their talk page to see if they've already been greeted (though there's no harm in greeting a new user again; you can always say "hi", and offer your assistance).
Check the recent changes. If there is a new user, it will say as an edit summary: (New user account). These users will also be on the account creation log. You can then click on the red linked talk page and then greet them. This is also helpful if you are looking for newbies, vandalism, etc.
Signing up to be a mentor here. You'll be automatically assigned to new users; you'll then be able to help them out and answer their questions. {{subst:Mentor welcome}} and {{subst:Mentor welcome-autosign}} can be used to welcome your proteges.
