How do I star emails on the new Gmail? There doesn't appear to be a star button anymore.

I still have a little star to the left of each message’s subject line. I don’t personally use the star system, but do you not still have stars next to the check box? Otherwise, I don’t know how you’d do it.
Sorry I can’t help more.

On the message list view, it’s to the left of the Sender’s name.
Inside an individual message, it’s under the [More] button.

Under Settings > Labels you have an option to show/hide stars.

on the new gmail it’s on the right by the date once an email is opened; on the left by the check box on each email line when viewing your inbox.