How do German articles and adjective endings work and what's the best way to learn them?

For me, getting to grips with adjective endings was a real turning point in my learning of German grammar and immediately made the language make a lot more sense! The concept can be broken down into four tables: the definite article table (the different forms of 'the' which indicate the gender and case of the noun), and three tables for adjective endings (depending on whether the noun follows 'a' or 'the' or doesn't follow an article at all!) Unfortunately the best way I've found of learning these tables is to simply memorise them, which at first may seem daunting and impossible, but becomes easier as you come to put them into practice. The aim of articles is to indicate the gender (masculine/feminine/neuter), number (singular/plural) or the case (nominative/accusative/dative/genitive) of a noun. When this isn't completely clear (e.g. the article indicating both feminine nouns and plural ones is 'die'), adjective endings help to distinguish and give us extra information about the noun. These are especially important when there isn't an article at all, for example 'kaltes Wasser' (cold water). Here's a diagram with the three sets of adjective endings and helpful examples: [can show this diagram on whiteboard]