I'm trying to create a sort of "trail effect" behind my player when it's moving. Something very similar to the one in this app https://youtu.be/W9ZP1i1CoRo. I don't know which approach could be the best or the easier. Could I use some particle effect? I think I can't since the effect is quite regular and not a kind of cloud or something. I would be very happy to do it without dealing with complex animations but if it is the only way please explain to me some basics.
The easiest way to do this is using particle effects. it's hard to give more information since every particle effect is rather specific to its' game's needs.
I suggest you take a look at the wiki. Also, take a look at this helpful video. It has a basic usage of the particle effect editor, as well as the usage of ParticleEffect objects in libgdx code.