In English, when you have a toothache, you go to the dentist. When you need a haircut, you spend an hour at the hairdresser's. You name the professional to refer to their workplace. Italian does the exact same thing, but it uses a preposition that often confuses learners.
Instead of using the typical prepositions for indicating a destination or a location, Italian uses da. If you translate it directly, it sounds like you are coming from the professional, but it actually means you are going to or staying at their place.
The preposition da usually translates to from. However, when it is followed by a person, a profession, or a title, it means you are at that person's house or workplace, or that you are going there. It handles both movement and location.
You must combine da with the definite article to match the professional. For example, medico is a masculine noun, so you combine da and il to make dal.
Oggi vado dal medico.
(Today I am going to the doctor's.)
Siamo dal dentista e aspettiamo il nostro turno.
(We are at the dentist's and we are waiting for our turn.)
Running Errands
Italian uses this structure for almost every local shop or service if you refer to the person working there. You can drop off your car dal meccanico, buy bread dal panettiere, or get a haircut dal parrucchiere.
La mia macchina è dal meccanico.
(My car is at the mechanic's.)
Compro il pane dal panettiere ogni mattina.
(I buy bread at the baker's every morning.)
The rule applies to female professionals and words starting with vowels, too. If your doctor is a woman, you go dalla dottoressa. If you need legal advice, you might go dall'avvocato.
Alle due ho un appuntamento dalla dottoressa.
(At two o'clock I have an appointment at the doctor's.)
Domani andiamo dall'avvocato.
(Tomorrow we are going to the lawyer's.)
The Professional versus the Shop
Watch out for the difference between the person and the building. If you mention the shop itself, you will usually use the preposition in. But if you name the professional, you must switch to da.
For example, you can buy medicine in farmacia (at the pharmacy) but you go dal farmacista (to the pharmacist's). You can buy meat in macelleria but you visit dal macellaio.
Vado dal farmacista per comprare le medicine.
(I am going to the pharmacist's to buy medicine.)
Oggi pomeriggio vado dal macellaio.
(This afternoon I am going to the butcher's.)
Il gatto sta male, dobbiamo portarlo dal veterinario.
(The cat is sick, we have to take him to the vet's.)
Summary
Whenever your destination is a person or a profession rather than a geographic place or a building, use the preposition da combined with the correct definite article.