Some sources for sample altar prayers include Catholic.org and Bible.org. Both of these resources feature a broad variety of prayers for all types of meetings and occasions, including Mass and personal prayers.
To begin praying, introduce yourself as a way to acknowledge God's presence, and establish a relationship with the source of your prayer. Understand the presence you are in, and be yourself. Anybody can pray, and you do not need to be a copy of a previous saint to form a union with God. When you pray, you are speaking with God on mutual terms, which means that you do not need to have any pretenses about the nature of the prayer or yourself.
When you are comfortable enough to begin praying, do not be afraid to ask for what you truly want. When you pray, you ask God for help, and you prepare yourself for his influence in the future. Before a prayer, be sure to stay humble and thankful, and when you start the prayer, give thanks to the things that God provides for you in your life, and understand that everything that was, is and will be possible are all results of him and his work.