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 different usage about the Zero Article.
Different usage
At times we don‘t use an article in German. That is then called zero article or Nullartikel (m).
Ich habe xxx Kinder. Die Kinder sind groß.
I have xxx children. The children are big.
Unfortunately, there are differnces between English and German when it comes to the Nullartikel. Here's a little insight into those differences. You don't have to memorize this at all. You'll pick this up as you go without any addional effort. This is merely FYI (for your information).
Different usage I
Article in German but not in English:
Ich fahre mit dem Bus. >> TRANSPORTATION
I go by xxx bus.
Du wohnst also in der Lindenstraße. >> STREETS & SQUARES
So, you live in xxx Lindenstreet?
Ich bin noch auf der Arbeit. >> WITH ARBEIT, KIRCHE, SCHULE, BETT
I am still at xxx work.
Different usage II
Article in English but not in German:
Ich spiele xxx Klavier. >> INSTRUMENTS
I play the piano.
Ich höre xxx Radio.
I listen to the radio.
Ich bin xxx Mechaniker. >> PROFESSIONS
I am a mechanic.
This topic is covered in: A1-L01, A2-L01 and B1-L01.