To give a Mormon a biblical case for the Trinity, the first step is to show there is only one God.
When making a biblical case for the Trinity, the first step is to show that the Scriptures clearly teach there is only one God. Passages like Deut. 6:4, Isaiah 43:10 and 44:6-8, and John 17:3 are very explicit about this point.
However, the common Mormon response is to claim that there is only one true God of this earth—there is only one God that Mormons worship, although there are other gods. So, respond with the following questions:
1. "Can you show me a verse that clearly states there is more than one true God?" The Mormon has just added a phrase to the biblical text which is not supported by the immediate context or the context of all of Scripture. Therefore, we want to put the burden-of-proof back on the Mormon.
2. "The LDS Church actually teaches there are 3 different gods of this earth: God the Father, God the Son, and God the Holy Ghost. Which God of this earth do you worship?" This question demonstrates the inconsistency of the Mormon's claim and can lead to other important discussions (e.g. Jesus accepting worship in John 20).
By the way, there are clear statements in the Book of Mormon as well, that support the idea there is only one God. See Alma 11:26-29, 44 and Mosiah 15:1-5 as examples.