Why the conditional is used?

[Hello] を日本語で何と言えばいいですか. Translation: how do you say "hello" in japanese?. Why is used the conditional in this question?

Because this is the standard grammatical pattern for this kind of thing.

If you start with the general case without asking the "what" question it might make more sense.
こんにちはと言えばいいです。→ It's good if you say "Konnichiha." (or, You should say "Konnichiha.")
お酒を飲めばいいです。→ It's good if you drink sake. (or, You should drink sake.)

Now consider the question with "what":
何を飲めばいいですか？ → What is good if I drink it? (i.e. what should I drink?)
何と言えばいいですか？ → What is good if I say it? (i.e. what should I say?)
[Hello] を日本語で何と言えばいいですか → What is good if I say 'Hello' in Japanese? (i.e. How do you say 'Hello' in Japanese?)

Isaac,

I want to emphasize that this particular form of the Japanese conditional, the ～すればいい form, is often translated into English as "should".

（どう)すればいい（ですか？) (What) should (I do?)

Your example, 日本語で何と言えばいいですか, could be translated as "How (should) I say this in Japanese?" (which sounds strange in English).

Another example:

この本を読めばいいですか？ Should I read this book?

In addition, ～すればいい is often paired with the phase でしょう to mean "I wonder if I should…"

この本を読めばいいでしょうか。I wonder if I should read this book.

彼女にこれを上げばいいでしょうか。I wonder if I should give this to her.

Another example of the Japanese conditional which works the same as ～すればいい is "～ったらいい" (meaning "should").

どうしったらいいですか？ What should I do?

どうしったらいいでしょうか。 I wonder what should I do.

彼女にこれを上げったらいいでしょうか。I wonder if I should give this to her.

(I also think the ～すればいい form is more polite than the ったらいい form, but I am not sure about this. Let's see what other people say.)

No idea about the comparison of ～ばいい to ～ったらいい. Seems like that would be neutral.
If I wanted to be more polite, I'd change いい to よろしい. Or throw an いかが in there. Depending on who is speaking to whom.

Thanks to all of you.

There is another similar expression "the dictionary form といい" (e.g. この本を読むといいです), but this expression is usually not used in a question, thus, お酒を飲むといいですか sounds a bit awkward.

As for ～たら conditional, It's "past form + ら", i.e., "What should I do?" is どうしたらいいですか. しったら means 知ったら, not the -tara conditional of する. Similarly, it's 上げたら for 上げる, not 上げったら.