Let S be a collection of subsets of a given set. These could be submodules, or ideals, or anything else for that matter.
Let W be an arbitrary nonempty subset of S, a collection of submodules for instance, and assume W has a maximal element. This means W cannot be an infinite ascending chain, and since W was arbitrary, S is noetherian. Conversely, assume some W has no maximal member. There is always another set in W that is larger, so build an infinite ascending chain, whence S is not noetherian.
Similarly, the collection S is artinian iff every subcollection W of S has a minimal member. The proof is the same as above, just run the chains down instead of up.