Broken chords are played with the same fingers you would use when playing a 'normal' chord.
You may find it hard, at first, to play these without accidentally pressing on all three notes at once, but with a little practice, you will soon get very used to it
In this C Major broken chord, the C is played using finger 5, and the E and G, are played together, using fingers 3 and 1, as shown in the video.