Anciently, making an oath or covenant was the strongest form of commitment one could use. When the Lord swears something to us, this should be very serious to us. Look for such language as "As I the Lord liveth," "I am the Lord," or when the Lord uses a certain Name (ie. "the Lord of Hosts is my name, or "Holy One of Israel," etc), or when he calls someone else by name with a promise: "Thou art Nephi . . ." "Blessed art thou Simon Barjona . . ." Prophets also give promises. When you find an oath or covenant, it is helpful to look for the conditions of the promise and also the consequences/blessings. Sometimes they are stated and other times they are implied.
Look For: Look for the words above that mark off covenant language.
Example: 1 Nephi 1:20 In the middle of the verse, Nephi makes an oath to those who are chosen of the Lord. The covenant language is when he states "I, Nephi." He promises us that the tender mercies of the Lord will deliver us if we are faithful. Thus, Nephi is swearing to us that God will fulfill this promise in our lives as the Lord has in his and his fathers.
The Old Testament is especially full of these examples of oaths and covenants. For example in Leviticus 19:18, the verse ends with the statement "I am the Lord." It may seem strange to us, but the Lord is making an oath to us. If we seek revenge or "bear grudge" against our neighbors, then it is as if we have done it unto Him. If we will love our neighbors as ourselves, then we will be favored by the Lord and He will love us.
(Adapted from Panning for Gold: Various Methods to Understand and Apply the Scriptures to Ourselves by Eric Bacon, Northwest Area Seminaries)