If I am not mistaken, the above sentence can either mean "I will eat fish" or "I eat fish".
... conjugating the verb to the ます form only aims to make the sentence polite and doesn't actually change the tense or meaning.
Correct. ます is a conjugation form that affects the social context of the sentence (indicating details about who is speaking and who is listening, and also sometimes who the sentence is about), but not the tense (i.e. the time when the action occurs) or aspect (i.e. the completedness, repetitiveness, etc. of the action).
... from just that one sentence (assuming someone tells me just that one sentence in the example), how do I determine what the tense of the sentence is?
Japanese has no future tense. It just doesn't exist as a feature of the language. Japanese is often described as having a past tense, where verbs end in -ta, and a non-past tense, where verbs end in -u. So in answer to your question, that one sentence is in the non-past tense.
Note that past tense itself is sometimes the wrong term for words ending in -ta. Consider a sentence like: 明日、このプロジェクトが終わった後、（なにか）しましょう / "Tomorrow, after this project has finished, let's do (something)." Here, 終わった clearly has the -ta ending, but we're talking about tomorrow, so it can't be about the past. This is where we instead have to talk about aspect: in this case, the -ta ending doesn't describe tense, or when the action happens, but rather aspect, which could be various other dimensions of verb-ness: completion, repetition, ongoing state, so-called "telic" action with distinct before-and-after states (like "change" or "pick up") or "atelic" action with no such clear distinction (like "work" or "sleep"), etc. etc.
More at Wikipedia about grammatical aspect, grammatical tense, and the non-past tense.