Vado a piedi al mercato ogni domenica.

• Vado is the first-person singular present of andare (“to go”), used when you move away from your current location toward another place.
• Vengo is the first-person singular present of venire (“to come”), used when you move toward the speaker’s (or listener’s) location.
In this sentence you’re talking about leaving home (or wherever you are) to reach the market, so you use vado.

• A piedi literally means “by feet,” i.e. “on foot.”
• Italian uses the plural for body parts in many fixed expressions (compare mi fanno male i piedi = “my feet hurt me”).
• It’s a set phrase for walking; you can’t say “a piede”—it must be piedi.

• Italian verbs are conjugated to show who is acting, so the pronoun is often omitted.
• Vado already tells you that the subject is “I.”
• You can add io for emphasis or contrast (e.g. IO vado a piedi, while someone else might not).

• In Italian a + il contracts to al before masculine singular nouns:
– a + il mercato → al mercato
• If the noun were feminine singular (e.g. stazione), a + la stays alla:
– a + la stazione → alla stazione

• Il mercato typically refers to an open-air or covered public market of individual stalls (fruits, vegetables, etc.).
• Il supermercato is “supermarket,” the kind of big indoor store with aisles.
• If you usually go to a supermarket, you’d say Vado in supermercato or more commonly Vado al supermercato (even though some speakers drop the article: Vado in supermercato).

• In Italian (as in English) the simple present expresses habitual or routine actions.
• Vado a piedi al mercato ogni domenica = “I walk to the market every Sunday.”
• You could also add di solito if you want: Di solito vado a piedi al mercato ogni domenica (“I usually walk to the market every Sunday”).

• Ogni always takes a singular noun: ogni domenica, ogni giorno, ogni anno.
• Tutte le domeniche is also possible and emphasizes “all Sundays,” but it feels a bit more formal or forceful.

Yes, both are fairly mobile:
• Ogni domenica vado a piedi al mercato.
• Vado al mercato ogni domenica a piedi.
• Vado a piedi ogni domenica al mercato.
Word-order changes can shift emphasis but the basic meaning stays the same.

Use in + vehicle for most transport:
• in macchina (by car)
• in autobus (by bus)
• in bicicletta or in bici (by bicycle)
So: Vado al mercato in macchina ogni domenica.