For a time of personal prayer, go to a place where you can have some privacy and just begin to talk to God the way you would talk to a friend. You can kneel, or sit, or stand, or lie on the floor. Some people walk about the room as they pray. You can close your eyes or pray with them open, whichever is best for you to concentrate on God and His presence with you.
You might want to start by reading a psalm of praise, such as Psalm 96, or another psalm that addresses God directly. After a brief time of worship, begin to ask God for whatever is on your heart. Then thank Him for listening to you and ask Him to answer your prayers.