$K$-means - how to calculate minimum distance

I was reading this article on $K$-Means and I got lost when it was time to assign objects to clusters. After calculating the centroids distance to every object, how can I calculate the minimum distance in other to assign objects to the nearest cluster?

-

Going through the article again, I found out that there isn't any need to find a minimum distance other than the distance between the centroids and other vectors. If the distance between a vector and two centroid A and B are 2.45 and 3.6 respectively, then the object is assigned to centroid A because of the lesser distance between them.

-