Welcome to the crash course in German adjective endings.
Admit it; you don't like learning tables full of endings, do you? Me neither. One of the most startling aspects of the German language is its amazing regularity and logic, and adjective endings (often taught as tables of 48 different endings with various complicated explanations as to when to use which) are no exception. Well, this is the real explanation: three simple rules, a few remarks and plenty of examples, and it'll all make perfect sense to you (or your money back). For this explanation you don't need to know much other than what an article is, what an ending is, and the endings of der/die/das (which you should get to grips with over the course of learning German).
- Rule 1. If the adjective has some sort of article or related word (der, eine, dieses, jenem, meiner, ihren) before it, then it takes a simple throwaway ending (see table below).
Simple, yes? (Exception: when the article is 'ein', in which case see rule 2. Also see remarks below.)
- Rule 2. If the adjective has no article before it (or just has 'ein', with no further endings such as 'einem'), the adjective takes the ending that the article would take if it was there. So if it's masculine nominative singular, the article is 'der' so the ending is '-er'. 'die' = '-e', 'das' = '-es', 'dem' = '-em', 'den' = 'en'.
(Exception: masculine and neuter genitive singulars. See remarks below.)
- Rule 3. Two or more adjectives modifying the same word take the same endings. Ein guter netter junger sympathischer Mann.
That's all. And it's easier even than that: there is a huge underlying logic underneath all these rules. The 'exceptions' aren't really exceptions when you know why and how all the above works, which is what I'll explain to you here.
Essentially, if there has been some sort of grammar conveyed by a non-trivial ending (and by 'trivial' I mean the really easy ones in the table in rule 1) on an article, the adjective (being a naturally lazy species) doesn't need to bother. If there hasn't been any grammar conveyed, then the adjective needs to do the work by taking an ending as specified in rule 2. Obviously, if there's no article then it hasn't conveyed any grammar, so the adjective will have to do so by taking an ending; 'ein' doesn't convey any grammar because it has no ending, so you need a non-trivial adjective ending as in rule 2, but 'eine', 'einem', 'einen' all do, so you just use the throwaway endings in rule 1, because the 'ein-' ending conveys some grammatical meaning, and the adjective is lazy and can't be bothered to. (See how my 'exception' in rule 1 wasn't really an exception now?)
This gives rise to one more small 'exception', mentioned in rule 2: 'der Preis kalten Biers'. As expected, though, it's not really an exception; even though there's no article there doing the '-es' genitive-y bit, there is an '-s' on the end of 'Bier'. So again the adjective doesn't need to do any work, because something else has already conveyed some grammatical meaning for it.
- Let's talk about beer. How would we say "the cold beer"? Well, we know from key stage 0.1 that it takes the form "das kalt__ Bier". What adjective ending should it take? Well, there's an article there, "das'", which is doing some grammatical work, so the adjective is going to be naturally lazy as in rule 1 and take a throwaway ending: "das kalte Bier". So far, so good.
- What if we now just want to talk about "cold beer" in general? Uh oh, "kalt__ Bier" - the "das" that was doing all the work has disappeared. There's no article or anything to convey any grammatical information any more, so "kalt-" has to do the work, and it adopts the "das" ending: "kaltes Bier".
- On the other hand, if we want to talk about "a cold beer" (and couldn't we all do with one of those right now? Just to get us into the German mindset...), we've got an article creeping in again, hooray! So it's of the form "ein kalt__ Bier". But hold on, "ein" doesn't do any grammatical work, because it hasn't got an ending. So yet again, "kalt-" will have to do the work of the "das" ending: "ein kaltes Bier".
- Now let's be eccentric and start talking about cold beer in the dative. (If it helps, imagine there's a relevant preposition with it: "I'm coming to the party with beer!".)
- So "with the cold beer" would be "mit dem kalt__ Bier". Well, again, there's a "dem" conveying some grammatical information, so the typical throwaway ending on the adjective: "mit dem kalten Bier".
- "With cold beer" would be "mit kalt__ Bier" - no article doing any grammatical work, so "kalt-" takes the relevant ending. The article would be "dem" if it had bothered to show up to the grammar party, but it didn't, so "mit kaltem Bier".
- "With a cold beer" would be "mit einem kalt__ Bier" - there's an "einem" conveying some grammatical information through its ending, so "mit einem kalten Bier".
- "With my cold beer" would be "mit meinem kalten Bier".
- "With this good, cold, tasty beer" would be "mit diesem guten, kalten, leckeren Bier".
Adjectives are lazy. They're trying to do the least amount of work possible, so whenever there's an article or a related word around that has an ending and therefore conveys some grammatical meaning, they just take one of the easy endings as given in the table in rule 1. They also slack off when there's an 's' on the end of a genitive, like "Biers", regardless of whether there's an article or not. But when there's no article (or an article like "ein" which doesn't have an ending), they're happy to take the ending of the relevant form of the article; if there's more than one adjective qualifying the same noun, they'll all take the same ending, so one adjective conveying grammatical meaning doesn't mean the next one will be lazy; this will only happen when an adjective follows an article (or related word) taking one of those endings.