What sort of transformation is a 3d cubic tensor?

Question

I was curious about tensors and higher dimensional matrices. I know what a tensor is. But I can find next to no readable information about what or how to actually work with them? In short, what kind of transformation is a say 2x2x2 cubic tensor? What are it's inputs and outputs? And there an analogue of matrix multiplication for 3d tensors that is analogous to composition of linear maps like it is for matrices? In general, can you extend other concepts from linear algebra into these 3d matrices? I know tensor problems in general are NP hard, but what about in the case of either cubic tensors or tensors of a fixed order? And even if they are NP hard, is it known what the generic complexity looks like? And are the problems efficiently computable in practice? I am a high school senior, but I am interested in higher math, so please don't make this too complex. I taught myself basic linear algebra on my own. I am fine with a long answer however, as long as everything is clearly defined.