Generally it comes down to reasonable interpretation, which is disputable. Some cases are easier to decide on than others. In the end it comes down to sensible judgement.

For example in the Apology, the first mention of "the gods" is this one:

"their hearers are too apt to fancy that speculators of this sort do not believe in the gods." οἱ γὰρ ἀκούοντες ἡγοῦνται τοὺς ταῦτα ζητοῦντας οὐδὲ θεοὺς νομίζειν.

"Gods" (θεοὺς, no definite article) is plural in this passage, so that makes it very likely he's referring to the conventional pantheon of gods rather than the philosophic concept of God-hood in general. Secondly he's talking about how the Athenians are accusing the philosophers of not believing in the city's gods. So it's more appropriate to translate it "the gods."

In the next passage, the word for a singular god with a definite article in front of it is translated as "the god":

"I will refer you to a witness who is worthy of credit, and will tell you about my wisdom - whether I have any, and of what sort - and that witness shall be the god of Delphi." τῆς γὰρ ἐμῆς, εἰ δή τίς ἐστιν σοφία καὶ οἵα, μάρτυρα ὑμῖν παρέξομαι τὸν θεὸν τὸν ἐν Δελφοῖς.

It wouldn't make sense to translate τὸν θεὸν as "God", because Socrates is calling attention to the particular: this is "the god of Delphi", that is, one of the many officially recognised gods. If the translator had it the other way, the phrase "that witness shall be God of Delphi" wouldn't make sense, since the philosophically supreme God is the God of the Universe, not merely Delphi.

In the passage below, ὁ θεὸς (singular god with a definite article) is rendered as "God":

"but the truth is, O men of Athens, that God only is wise; and in this oracle he means to say that the wisdom of men is little or nothing." τὸ δὲ κινδυνεύει, ὦ ἄνδρες, τῷ ὄντι ὁ θεὸς σοφὸς εἶναι, καὶ ἐν τῷ χρησμῷ τούτῳ τοῦτο λέγειν, ὅτι ἡ ἀνθρωπίνη σοφία ὀλίγου τινὸς ἀξία ἐστὶν καὶ οὐδενός.

It feels more natural to render ὁ θεὸς as "God" because, even though he is talking about the answer of the god at Delphi, he makes a general statement about the moral goodness of God-hood: "only God is wise." It would make no sense to render that as "only the god is wise", because it implies that only that particular god at Delphi is wise, and presumably all the rest of the pantheon isn't wise. What he means is that the divine beings are wise, but humans aren't. Perhaps he could have gotten the same point across if he had said "only the gods are wise", but he chose a singular to emphasise the one-ness of the supreme divinity, and so the translator respects that choice by translating it as "God".

I hope that helps give a sense of why one phrasing is chosen over the other in different circumstances. In most cases, it's not grammar that clears it up, but sense.