What exactly do you want to scale? But in the end the answer is likely "connection pooling", either integrated in the application or with a dedicated pooler like PgBouncer which this article is about.

For Postgres a good way to scale is to just use a bigger server. You can get a lot of very fast storage and lots of CPU cores inside a single server today. And if that isn't enough you're far, far into territory where you can't give generic answers and it depends a lot on your specific use case and what you do with that database.