When you are asked to decline an article or a noun, you are simply being asked to give its different forms for the different genders and cases in question.
For example, here are all the declensions of ein and der:
The declensions of the indefinite article
The declensions of the definite article
Thankfully, unlike in Latin (shudder) almost all of the nouns in German don’t decline at all. The exceptions to this are weak masculine nouns, which change only slightly, adjectival nouns, and one final crazy exception which doesn’t abide to any but its own renegade rules: das Herz. Lessons on all these things coming soon!