Can you explain adjective endings to me?

Like every grammar topic in German, adjective endings become more intuitive the more you read and write. One possible (and possibly tedious) way of learning them is through memorising grammar tables, but I'll explain here a fairly simple and logical process to crack them every time.

Adjective endings complement the gender of the noun, and are dependent on whether or not there's a definite article (der, die, das, etc.), an indefinite article (ein, eine, einen, etc.) before the noun.

The first step, therefore, is to look to see if there is an article, definite or indefinite, before the noun. If there is, then head straight on to step 2. If there isn't, one simple way of looking at which adjective ending to use is to think: "if there was an article there, what would it be?" For example, if I want to talk about the 'British Parliament', I'll look at the gender of the noun (das Parlament), see that it's neutral, so I'll add the 'neutral' ending to the adjective ("-es") - so we end up with "Britisches Parlament". This also applies to articles that are changed by the case, i.e. if the dative definite article was "dem Parlament", here we would have "Britischem Parlament".

If there is an article before the noun, we move onto the second step: is the definite article in its original form? In other words, is there article true to the gender of the noun - do we have "der", "die", "das" or "ein", "eine"? If the answer is no, i.e. we have "dem", then simply add an "-en" to the ending of the adjective. For example, "dem britischen Parlament".

If the article is in its original form, we have have another easy step. Third: is the noun plural? If so, simply add on -en. For example, "die kleinen Hünde" - Hünde is the plural of "der Hund", so we simply add on the -en. 

The last step is to consider if the article shows the gender of the noun. This applies to indefinite articles, "ein" and "eine", but as "eine" shows the gender of the noun (feminine), this last step is really if you're left with "ein", so masculine and neutral nouns. Again, the solution is simple: a masculine noun will have the ending "-er" (as is "der"), and the neutral nouns will have the ending "-es" (as in "das"). For example, "ein kleiner Hund" or "ein großes Bier". 

Finally, if you've gone through all the steps and still haven't found an adjective ending, simply add "-e". For example, "der kleine Hund", "das britische Parlament".

If you have any difficulties or questions regarding this topic (or any other German topic), please don't hesistate to get in contact.