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I've just read Arora's paper "Polynomial Time Approximation Schemes for Euclidean TSP and other Geometric Problems". On page 8 Arora says that the dynamic programming procedure can be changed to get a algorithm for the k-MST-Problem.

I don't not understand how this is done. Any ideas?

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What have you tried ? give us your ideas. How does the algoritm of Arora work .. – AJed Jan 9 at 20:11
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Do you understand k-TSP? Do you understand MST? If so, then you probably understand k-MST (judging from a cursory look at the paper). Therefore, can you refine your question as to which of these two you don't understand? – Yuval Filmus Jan 9 at 21:51

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