How does hydrogen bonds cohesion and surface tension allow some insects and animals to walk on water?

The answer is pretty simple, and has to so with properties of water, mostly, not insects. Water molecules are polar molecules containing Oxygen and Hydrogen. This allows them to form hydrogen bonds when in close proximity to each-other (hydrogen bonds are a strong type of Inter-molecular force.) The molecules on the surface, however, have less water molecules near them, and so form stronger hydrogen bonds with nearby water molecules. Some insects, like the iconic water strider, have large feet to displace their weight over a large area, and thus avoid breaking the surface hydrogen bonds, which allows them to "walk on water."