Chain signals before an intersection; regular signals after those, and on the track to split the track for multiple trains simultaneously.
See: https://wiki.factorio.com/Tutorial:Train_signals if you haven't already.
I frequently set up tracks with segments as large as my longest train, but then end up having to add an intersection here or there, breaking up segments into smaller sizes. This is the root of most of my train woes (aside from LTN issues, which are a whole other issue!)
That's what chain signals are for. If a train waiting at a signal causes issues, replace the previous signal with a chain signal to prevent the train from problematically waiting at the signal.