Wiktionary
go steady
vb. (context intransitive dated English) To date one person regularly and exclusively.
WordNet
Usage examples of "go steady".
Any time we saw a man starting to go steady with a girl, we made life miserable for him.
He'd have to go steady if the siege was going to be a long one, and it could well last until the snow had melted.
His nerves were all over the place and on the drive down he had touched ninety before Smiley sharply told him to go steady.
Me and Brant used to go steady and he was asking about the breakup.