I was looking through some text about finding the EMST (Euclidean MST) using Delaunay triangulation technique, but also read somewhere that the EMST can be found through a sweep
I think the simplest technique for finding Euclidean minimum spanning tree is Delaunay trinangulation, use Bowyer-Watson algorithm. It is very easy to implement, once you have that, you can just use something like Kruskal's algorithm, using the distance as the edge weight.