Is there an easy way to tell how gravity works?

Science only “explains” things by reducing them to explicit mathematical descriptions. General relativity explains gravity as the warping of spacetime by giving a set of equations in which the space-time distribution of mass-energy can be inserted and the equations then solved for the curvature of spacetime. This theory has proven highly accurate. So any other theory must give the same answers over the domain in which GR has been tested. But GR is incomplete in two respects. First, it is inconsistent with quantum mechanics. Unfortunately, this can only show up in very extreme gravitational fields, such as near a black hole, so it is hard to test. Second, if gravity exists as a quantum field there needs to be some description of how it interacts with other quantum fields, a quantum description of spacetime. Andre Sakharov proposed a theory in which vacuum fluctuations interact with mass-energy to produce gravity and Padmanabhan and Verlinde have pursued versions of this theory and shown that it is equivalent to GR for weak fields.

So it depends on what you mean by “other way”. There’s not going to be an “other way” that disagrees with GR except in extreme circumstances, just as GR only disagrees with Newtonian gravity in a few unusual circumstances. NASA still uses Newtonian gravity to plan it’s missions.