Is it best to let the paints dry on their own or is there a trick of the trade for quicker drying times?

If you mean how to get acrylic paints to dry faster, the answer is easy. Just add more solvent to your paint! Here’s what happens when we use thinner paint and more of it:

1. The pigment particles are on average smaller. Because these particles are lighter in weight than solvent molecules, they stay suspended in the liquid longer and have a better chance of getting knocked into other pigment particles by a solvent molecule bumping them around. This makes for a smoother looking final film of paint (in other words, fewer steps between initial droplet of pigment hitting the model and final smooth appearance). When there is less solvent in the mix then pigment particles tend to clump together due to van der Waals forces, and as you can imagine, it’s difficult to get a smooth final finish with clumps of dry pigment stuck together
2. The paint is thinner, so drying happens faster because there are fewer solvent molecules per square inch/centimeter in the mix. These have higher average speeds than those that do not interact with the pigment particles so they bump them around more frequently, creating more opportunities for pigment-pigment collisions. More collisions means better final film smoothness due to greater likelihood that there will be multiple pairings before the next collision event (for example: let’s say I want four steps between initial droplet of pigment hitting model and final smooth paint appearance). This gets rid of streaks, lines, bumps and other anomalies quicker.
3. The original paint tends to have fewer “contaminants” in it, which are really just particles of pigment that didn’t mix well with the other particles in the mix. That means less partially dried paint flaking off your model while you’re painting, and usually a more desirable final appearance.