Just a couple of comments about the use of articles, since you were finding this confusing. I'm going to be really basic here in places, but don't feel insulted; I find that students get so overwhelmed by rules that it's easy to lose sight of the underlying workings of the language & it sometimes helps to be reminded of what they already know.
The function of the article is to pick out a specific thing ("the man"--i.e., perhaps the one mentioned earlier in a conversation--vs. any random man).
In addition, the article can do other useful things, namely: it can help to group words together in a sentence. There are several important points to note.
1) the significance of attributive vs. predicative position
Attributive is another way of saying the subject of the sentence. In a sentence where the only verb (written or understood) is the verb "to be" any nouns or adjectives that are predicative rename the subject: "The man (subj) is good (predicative)"; "honesty (subj) is a virtue (predicative)". In English we mark subject and predicate using word order. Greek is somewhat more flexible. Often the presence and location of the article will help you to sort out how things belong together.
If you have a noun and an adjective and an article that agree with each other, there are several possibilities about how they may be ordered.
ὁ ἀγαθος ἀνθρωπος
ὁ ἀνθρωπος ὁ ἀγαθος
In both of these, the adjective is in attributive position ("the good man", no "is" implied). The key thing to note here is that the article acts a bit like a sandwich linking the adjective to its noun.
Compare it with the following:
ἀγαθος ὁ ἀνθρωπος
ὁ ἀνθρωπος ἀγαθος
Here the adjective is outside the article+noun sandwich: predicative position ("the man is good")
If there's no article at all you have to figure things out from context.
2) Sometimes the article will also be used to group other words with belong with the noun. Again, the sandwich principle is at work: if you stick something between the noun and its article, it indicates that the words in between somehow relate to it. Often this will be either possessive nouns or prepositional phrases:
το θεου δωρον ("the gift of the god"). This could of course also be written το δωρον θεου, but the writer may want to avoid any ambiguity and link the gift closely with its divine origin.
οἱ ἐν τῇ ἀγορᾳ ἀνθρωποι λεγουσι ("the men in the agora are talking"). Again, this could be placed outside the noun, but there may be reasons to emphasize that "in the agora" picks out a specific group of men, rather than the location of the activity. Compare the following:
οἰ ἐν τῇ ἀγορᾳ ἀνθρωποι λεγουσι, οἰ δὲ ἐν τῃ οἰκία σιωπασιν ("The men in the agora are talking, the ones in the house are silent." Two groups of men doing different things.)
οἱ ἀνθρωποι λεγουσι ἐν τῇ ἀγορᾳ, ἐν δὲ ταις οἰκίας σιωπασιν ("The men talk in the agora, but they are silent in their houses." One group of men with different behavior depending on where they are.)
3) When there is no noun that is goes with the article, it may be used to create a noun out of an adjective or prepositional phrase (substantive use of the article) where the noun can be understood from the context. This follows logically from point 2 above. Thus you have οἱ καλος καὶ ἀγαθοι ("the beautiful and the good", i.e., the nobility), or in the example I gave above, the men in the house (οἰ ἐν τῳ δομῳ).
IPHIGENIE: Kann uns zum Vaterland die Fremde werden?
ARKAS: Und dir ist fremd das Vaterland geworden.
IPHIGENIE: Das ist's, warum mein blutend Herz nicht heilt.
(Goethe, Iphigenie auf Tauris)