Without article it's mostly the same as the definite article ending would be ("strong" declension: shows the gender/case of a noun). With a definite article you already have an identifier to show the gender, so now you only have "gute" for singular Nominative and Accusative (except masculine Accusative) and "guten" for everything else.
With ein-words (mein and euer included) it is almost the same as with a definite article, only you need strong declension forms when the article is the same as in Nominative ("ein", "kein", "sein", "euer" etc.)
Would be good to have a lesson exactly on that...
There is a good rule to follow. Someone has posted it in Duolingo before. - if you have der/die/das - adjectives end on "e". - if you have ein/kein/mein - end of the word depends on the gender. - if you have plural form or a change in Akk., D. - word end on "en". These are the main rules and in this form are easy to remember.
Somebody linked this in another forum post: http://en.wikipedia.org/wiki/German_declension#Attributive_adjectives
This has been the biggest help to me through this particular lesson.