It's comparatively easy (cum grano salis) to grasp the following concepts:
- Euclidean space-time (continous space and continuous time)
- classical mechanics (discretely distributed matter in continous space and continuous time)
- Minkowskian space (continously intermingled space and time)
- special relativistic mechanics (discretely distributed matter in continously intermingled space and time)
- classical electrodynamics
- classical quantum mechanics (discrete energies, continuously distributed matter in continous space and continuous time)
- quantum electrodynamics
- general relativity (continously intermingled space-time and matter)
Accordingly, there are lots of introductory texts and text-books.
It's also easy to grasp
- numerical simulations (on artificially - and mostly unphysically - discretized spaces, times, and space-times)
- cellular automata (on unphysical regular spatial grids)
It's definitely hard to grasp (for somehow graspable reasons)
- quantum gravity
I do not know whether there are empirical evidences for a discrete space-time or only theoretical desiderata, anyhow I cannot figure a discrete space and/or time out.
Why is it so hard to introduce and explain the concept of a physical discrete space-time?
Why are there no easy to understand introductory texts or text-books on definitions, concepts, models, pros and cons of discrete space, time, and - finally - space-time?
Respectively: Where are they?
Are the reasons for this maybe related to the reasons why quantum gravity is so hard to grasp?