The tidal bulges are easy to understand if you think through a force diagram with the different forces on the various parts of the Earth. The gravitational force is weaker on the more distant parts of the Earth from the moon.[1]

So everything is pulled towards the moon, but the more distant parts are pulled less, and the sides are pulled inwards, so the resultant shape is the familiar ellipsoid

[1] http://nicholasbsullivan.com/page_oceanography/Meeting6/01_t...