He is so happy that he doesn't know what to say.
The grammar here is similar to the "so + adjective + that" form in English.
Here, 高兴得= is so happy that
After "that" or "得" comes the result. What's the result of him being so happy? The result is that he doesn't know what to say.
He is so fierce that nobody dares to make friends with him.
He is so excited that he can't sleep.
The exam was so difficult that everyone failed it.
I'm so hungry that I can finish ten bowls of rice.