In Supabase, the connection pooling system sticks to the PostgreSQL standard. Basically, you can set the maximum number of client connections to your database. By putting a cap on your database connections, you can manage your server's resources better and avoid performance hiccups when traffic spikes.

Before you tweak the connection pooling settings, you need to get to the settings panel in the Supabase interface. Here's how you do it:

• Head over to your Supabase dashboard.
• Click on the project that has the database you want to adjust.
• Pick the 'Database' tab from the side navigation panel.
• Inside the database tab, click on the 'Settings' option.

You'll find the configuration options for the connection pool in the database settings panel:

• Look for the 'Connection Pooling' section. This is where you can set how many client connections your database should handle at once.
• Change the ‘Max client connections’ field. The number you choose depends on your website's size and the traffic you expect. But be careful not to set it too high, or you might overload your server and run into performance problems.

Adjust these settings based on what your application needs and your specific operational requirements.

Changes to the connection pooling settings aren't saved automatically. To apply these settings:

• Double-check the changes you made to the 'Max client connections' field.
• Click on the 'Save' button, usually found at the bottom of the settings page.

Once saved, your database will use these new settings to manage client connections. Keep an eye on your system's performance and tweak these settings as needed to keep your database running smoothly.

Remember, managing database connections effectively is key to keeping your application running smoothly. Balancing user demand and server capacity ensures your app stays responsive and delivers a top-notch user experience.