The book of Psalms is a great example of personal worship. Consider King David; he was a song writer and the psalms of David are songs written in worship unto God. May these verses and various other verses from the book of Psalms inspire you to write your own songs of worship unto the Lord.
For you shall worship no other god: for the LORD, whose name is Jealous, is a jealous God:
Give to the LORD the glory due to his name; worship the LORD in the beauty of holiness.
O come, let us worship and bow down: let us kneel before the LORD our maker.
Exalt you the LORD our God, and worship at his footstool; for he is holy.
Exalt the LORD our God, and worship at his holy hill; for the LORD our God is holy.
All nations whom thou hast made shall come and worship before thee, O Lord; and shall glorify thy name.