Kruskal's Algorithm - Pseudocode

Here is Kruskal's algorithm:

function kruskal(n, edges):
    sort edges by weight ascending
    parent = array [0, 1, 2, ..., n-1]
    mst = empty list

    for (u, v, w) in edges:
        rootU = find(u)
        rootV = find(v)
        if rootU != rootV:
            mst.append((u, v, w))
            union(rootU, rootV)
            if mst.size == n - 1:
                break

    return mst

You will add exactly $n-1$ edges if the graph is connected. The Union-Find operations ensure you never create a cycle.