The source code is written in st-steiner.c. The sample input available on the website is copied in heuristic/input.gr. To run the program on the sample input, execute ./run.sh. The original input is available here

• reduce all the non-terminals with degree 2 (if a terminal has degree 2, then reduce its non-terminal neighbors so that they are of degree at least three. Update the new weights accordingly.)
• return the MST of the reduced graph
• if a leaf of the MST is non-terminal, delete it. Then the MST will have all terminal leaves. (see what might go wrong after here)
• what next?

Good luck.

Edit:

Here is a paper on the possible reductions.

Here's an earlier steiner tree competition stp.