Question

If you drop a metal paperclip into a cup of water, it will sink to the bottom. However, with practice, you can gently place a metal paperclip on the surface of the water and it will balance or appear to float. Explain why this happens.

Answer 1

If you drop a metal paper clip into a cup of water, if the surface tension of the water is more than the weight of the paper clip; it floats otherwise it sinks.
The surface tension acting on the paper clip depends on the length of the paper clip. If we place it gently on the water without completely immersing, but just touching it on the water surface so that most of its length stays in contact with water but not immersed, the surface tension acting on the paper clip will be higher and it will float. 

Answer 2

If we drop a metal paper clip in water it will sink because it disturbs the surface tension of water and the weight of the clip is more than the amount of water displaced by the body(however it is not significant in this case).
When we try to keep the clip gently on water then it will not sink as the surface tension of the water is not disturbed so it will appear to float but if we touch the water the clip will sink as the surface tension is agitated.