What are Der-words?
Well, here's what they are not: they aren't der, die, and das (the words for "the"). "Der-words" in German refer to a group of adjectives that, in English, include relative pronouns and a few other words:
dieser (this, these)
jener (that, those)
jeder (every, each)
All of these words follow a common declension pattern. The only exception is for alle, which only takes plural forms.
How Do the Endings Work?
Here's how the endings work. Just take the -er (or the -e for alle) off to find the stem. Because these are all adjectives as far as the part of speech goes, they will match the noun that they modify.
In case order (nominative, genitive, dative, accusative), here's how the different genders take endings:
Masculine: -er, -es + -s, -em, -en
Feminine: -e, -er, -er, -e
Neuter: -es, -es + -s, -em, -es
Plural: -e, -er, -en + -n, -e
Just for clarification, the notation "-es + -s" refers to the fact that, if the noun being modified does not already have an "s" on the end, an "s" is added to show the genitive case. And so "This man's job" would be translated as "Der Beruf dieses Mensches."
English: Which car are you taking today?
German: Welches Auto fährst Du heute?
English: I will take the dog to that new veterinarian in the city.
German: Ich werde den Hund zu jenem neuen Tierarzt in der Stadt.
English: Every day you need to do your homework for this class.
German: Jeden Tag mußt Du Deine Hausaufgaben für diese Klasse tun.
English: We have never seen such chaos before today.
German: Vor heute haben wir niemals solchen Wirrwarr gesehen.
As you can see, these adjectives operate in German in much the same way as they do in English. Memorizing the endings will make der-words a crucial part of your vocabulary, as they are used quite commonly in everyday conversation.