If you are beginner then I recommend you to start density based clustering so that initial value of K isn't required. You can initially start dbscan clustering using epsilon=10 and minpts= 5 and then check the number of generated clusters. After that, start a smooth increase of epsilon (11, 12, ... 15) and decrease of minpt (4, 3, ..1) and check the number of generated clusters each time. Then the average of these numbers are supposed to reflect the average number of real clusters.
But if you need to apply k-mean clustering then you might find Selection of K in K-means clustering paper useful.