The normal word order in both French and English is "subject + verb," as in il dit (he says). But in certain situations, such as asking questions and using quotations, it is very common in French to switch the order to "verb + subject": dit-il. This is common in English as well: "They are going to the concert" versus "Are they going to the concert?" This switch from "subject + verb" to "verb + subject" is known as inversion.
In French, most instances of inversion occur between pronouns and verbs. When a pronoun and its verb are inverted, the two must be joined with a hyphen:
Eh bien, mon garçon, dis-moi, que sais-tu?
Well, my boy, tell me, what do you know?
"Non, je ne veux pas sortir avec toi", répond-elle.
"No, I don’t want to go out with you," she responds.
When inverting a third-person pronoun (il, elle, on, ils, elles) and verb, you must pronounce the two with a liaison (see our lesson on liaison here). Thus we have "dit-Til," "répond-Telle," "est-Til," and so on.
When a third-person singular verb does not end in a t or d, you must insert a -t- between the inverted pronoun and verb. This inserted -t- does not have any meaning by itself; its sole purpose is to create the liaison:
A-t-il peur du noir?
Is he afraid of the dark?
Combien d’années, combien de siècles faudra-t-il, avant que ne se retrouvent pareilles constellations?
How many years, how many centuries will be needed before such constellations can be found again?
Captions 3-4, Il était une fois...: L’Homme - Part 6
For third-person plural verbs, the final t (which is usually silent) is pronounced in inversion:
ils donnent ("they give," pronounced like il donne)
donnent-ils (pronounced "donne-Tils")
In other words, all inverted third-person pronouns must be preceded by a t sound.
The first-person pronoun je is rarely inverted, except in interrogative constructions such as puis-je... (may I...), dois-je... (must I...), and suis-je... (am I...).
Although not as frequently as pronouns, nouns can also be inverted with their verbs, as the above example demonstrates (se retrouvent pareilles constellations). In this case, a hyphen is not required:
"Non, je ne veux pas sortir avec toi", répond Christine.
"No, I don’t want to go out with you," Christine responds.
A common way to ask questions in French is to use a "double subject," in which a noun is followed by an inverted verb and pronoun. This can be seen in the title of the video Alsace 20: Pourquoi le bio est-il plus cher? (Why is organic more expensive?) and in this caption:
L’art, est-il moins nécessaire que la science?
Is art less necessary than science?
Caption 3, Micro-Trottoirs: Art ou science?
Although the inversion method is a bit more concise, these two questions could easily be rephrased with est-ce que:
Pourquoi est-ce que le bio est plus cher?
Est-ce que l’art est moins nécessaire que la science?
To learn more about asking questions in French, including some notes on inversion, see this page.