Electrical ground works the same way mechanical ground works. The further off ground something is, the springier or softer its ground reference. Compare machine bolted to concrete pad, versus teetering on top of a flagpole. Works the same way here, with beams replaced with traces, beam cross-section replaced with trace width and height over the ground plane (wider and lower is stiffer), and beam length equal to trace length, and the resonant frequencies being shifted up a few half dozen orders of magnitude (nanoseconds vs. seconds, say).
The main quirk is that, in electronics, we can make a ground at any voltage -- mechanical analogies to capacitors and inductors are somewhat imperfect. With enough capacitors, we can make an elevated node behave near enough to "ground" for all intents and purposes (whereas this is harder to do with, say, skyscrapers, that tend to wobble in the wind).
What you want to do for signal traces is, fan them out around the supply pins so you have space to put a bypass cap in there. The bypass cap goes from the VCC pin to GND. GND is poured on the bottom side, so it can link back to the chip through vias on GND pins. Power is routed to the VCC pins wherever it fits, but be careful not to cut up the ground pour in the process -- a trace leaves negative space in the pour around it. Prefer routing (signals and VCC) on top side, with bottom side reserved for GND, and short crossing traces as needed.
Put lots of vias between GND pours on both layers -- this is analogous to building a parallel pair of trusses, and using just a few stringers between them for stiffness (hardly does anything), versus regular diagonal bracing (highly effective). Analogously, you don't need a massive swarm of vias, just one every so often (10-30 mm?) will do, plus any hot spots (three or four at trace crossings, one at the end of a peninsula, etc.).
Tim