How would you get a highscore visible within a game and for the game to be able to remember the score?

I am making a game with unity and am having troubles trying to get the highscore to be visible like in the old style arcade games

To get it visible, you could do a GUI box or label in the OnGUI function. In order to save the high scores, you could write an XML file, or any other file, or you could use Unity’s PlayerPrefs.