Get the conductor on the delayed train to endorse your ticket proving the train ran late (or give you something saying so, if you have a digital ticket).

When the train arrives, if your next train is a "reservation only" service, you should go to the desk of the train operator, show them your ticket from the late-arriving train endorsed with the delay and your ticket for the outbound train that you've missed, and they'll give you a new ticket for the next train with availability.

If the next train isn't a "reservation only" service I usually just get on and sort it out with the conductor. I think technically you're not supposed to do this, but it saves time so can allow you to take an earlier train, and I've never had a problem doing it. YMMV!

I've done this probably 8 times, and never encountered someone who couldn't speak English well enough to understand the situation. In fact, very little communication is necessary since you're holding an endorsed ticket showing your incoming train was late, and a ticket showing your outbound train that you've missed – there's only really one thing you could be asking for!