Morning prayer is probably Liturgy of the Hours, which all priests are required to pray. But it is a great devotion for anyone. It consists of psalms, canticles, and other scripture readings for the day. Here’s morning prayer for tomorrow morning:
universalis.com/20120604/lauds.htm
People who pray this daily have a book or books they follow. It’s a beautiful devotion if you have the chance to go. Even if you don’t have the book, it can be fruitful to go. I’ve attended when I didn’t have my book with me, and often a kind person will share their book with me so I can follow along. If not, you can listen. This can also be prayed alone, but it’s wise to learn from a group since it feels complicated at the beginning.