Sure, for the start you’ll need an Aseprite file with multiple layers, it can have multiple frames as well if you want some (or all) of your layers to be animated.
Then you got to the Edit > FX > Parallax and a new window pops up, there you can see a list of all of your layers. Each one of them has a Distance value specified, just as in real life - layers that are further away (higher distance value) move slower than the layers that are closer (smaller distance value). Note that layers with their Distance set to 0 will stay static and won’t move at all.
To change how fast, and in what directions the layers will move in the generated animation, there are two values for Speed in the Movement section.
You can see how layers will align in motion by moving the Shift slider in the Preview section.
Finally, you can specify how many frames do you want to generate in the output animation, currently, there’s no option to generate perfect loops automatically but it is planned for the future.
All of this is shown in the last image from the description, if you’d have any further questions - let me know. ✌️