Scripture quotations unless otherwise noted are taken from the Holy Bible, New Living Translation, © 1996 by Tyndale House Publishers, Inc.

When praying, instead of thinking only of yourself, pray as though your were praying with everyone in mind who lives on earth, that is, universally.

Be aware mentally that you are praying as though you were all the people in the world.

For example, when you are saying the following words of the Lord in Jeremiah, don't just think of it relative to yourself, rather, think of it relative to everyone in the world as you say it.

For I know the plans I have for you. They are plans for good and not for disaster, to give you a future and a hope. In those days when you pray, I will listen.
Jeremiah 29:11-12 

Likewise, when you are praying the 23rd Psalm, paraphrase it mentally in the following way. 

The Lord is our shepherd; we have everything we need. He lets us rest in green meadows; he leads us beside peaceful streams. He renews our strength. He guides us along right paths, bringing honor to his name. Even when we walk through the dark valley of death, we will not be afraid, for you are close beside us. Your rod and your staff protect and comfort us. You prepare a feast for us in the presence of our enemies. You welcome us as guests, anointing our heads with oil. Our cups overflow with blessings. Surely your goodness and unfailing love will pursue us all the days of our lives, and we will live in the house of the Lord forever.

Take this mindset with you as an option when you pray. Then you can be praying universally, for all the people in the world!