Garg (FOCS '96) gives two approximation algorithms for the minimum-cost tree spanning $k$ vertices in an undirected graph. Recently Jain and Vazirani (JACM '01) discovered primal-dual approximation algorithms for the metric uncapacitated facility location and $k$-median problems. In this paper we show how Garg's algorithms can be explained simply with ideas introduced by Jain and Vazirani, in particular via a Lagrangean relaxation technique together with the primal-dual method for approximation algorithms. We also derive a constant factor approximation algorithm for the $k$-Steiner tree problem using these ideas, and point out the common features of these problems that allow them to be solved with similar techniques.