The metric tensor is a key concept in general relativity, necessary to describe black holes, gravitational waves, the expanding universe, and other interesting and important phenomena. Unfortunately, it is usually presented either very superficially or in a highly technical and mathematical way. I have begun creating tutorials to help students develop a deeper understanding of the metric and a greater facility with its use, focusing on upper-division undergraduate students. Analysis of student behavior when working with drafts of the tutorials, combined with post-instruction interviews and testing with a novel metric, suggest that these tutorials show promise to be effective for introducing students to general relativity. In this preliminary study the tutorials increased conceptual understanding, developed mathematical facility, and instilled the attitude that general relativity is an approachable subject.