For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
Petition, thanksgiving, and requests are three ways we can pray as listed in Phil 4:6. Petitions are our needs or plea for relief in dire circumstances, such as 'give us this day our daily bread', or 'heal us in affliction.' Thanksgiving is thanking God for His blessings in general or specific. Requests are similar to petitions, but they are not necessarily requests for relief. It might be something like, "If it is according to your will, let this interview go well" or "please give me guidance."
Examples:
Requests - I John 5:14-15: "This is the confidence we have in approaching God: that if we ask anything according to his will, he hears us. And if we know that he hears us—whatever we ask—we know that we have what we asked of him."
Petitions - James 5:14 "Is any one of you suffering? He should pray."
Thanksgiving - Philemon 1:4 "I always thank my God as I remember you in my prayers, because I hear about your love for all his holy people and your faith in the Lord Jesus."