Luckily, the German article is used mostly the same way in English, but you might want to pay special attention to the few situations where it is different from English. Just some examples:

Identical usage

Ich sehe ein Auto. Das Auto ist grün.
I see a car. The car is green.

Ich sehe eine Lampe. Die Lampe ist schön.
I see a lamp. The lamp is beautiful.

Ich sehe ein Handy. Das Handy ist schön.
I see a mobile phone. The mobile phone is beautiful.

That's about it. If you are in doubt whether to use "a" or "the" just remember what you'd use in English. If you are in doubt whether or not to use an article at all, check the next chapter about the Zero Article.