da to describe relationships in space (depending on the context translated with to or at)
Vado dal medico.
I go to the doctor.
Oggi andrò da una psicologa.
Today I go to a psychologist.
Abito da mia nonna.
I live at my grand-mother.
da to add an infinitive or a indefinite pronoun
Indefinite pronouns we know already from chapter 7, they stand for something, but the thing they stand for is unknown.
There is nothing to eat.
Surprisingly an infinitive is added to an indefinite pronoun with a different preposition than an adjective.
That's the case in every language, although the philosophies behind are different.
infinitive: Non c' è niente da mangiare.
adjective: Non c' è niente di bello.
infinitive: Il n' y a rien à manger.
adjective: Il n' y a rien de beau.
infinitive: Non hay nada para comer.
adjective: No hay nada hermoso.
infinitive: There is nothing to eat.
adjective: There is nothing beautiful.
infinitive: Es gibt nichts zu essen.
adjective: Es gibt nichts Schönes.
If you take a closer look at construction like "niente di bello", "rien de beau", "nada hermoso", "nothing beautiful", "nichts Schönes" you see that the philosophies behind these constructions are different. Italian and French ("niente di bello" / "rien de beau" => literally: nothing of the beautiful) assume a collective (the beautiful in general) and of this beautiful there is nothing. Spanish, English and German see it in a different way. In these languages nada / nothing / nichts is an indefinite pronoun, stands for something and this something has an attribute which characterizes it. The constructions are completely different: There is nothing beautiful <=> Nothing that is beautiful. Although the English, German and Spanish construction is correct, they are not very logical from a grammatical point of view or in other words they are contrary to the system because normally a pronoun can't have an adjective (~I see the angry him~). From a grammatical point of view the French and Spanish structure is more logical.
Structure of the kind "Non c'è niente da mangiare", "Il n'y a rien à manger", "No hay nada para comer", "There is nothing to eat" are very strange from a grammatical point of view. This kind of structure is not difficult to use, you hear them one time and afterwards you will be able to use them. There is no problem from a practical point of view, but from a theoretical one. Structures like these are, in theory, complicated.
Non c' è niente da mangiare.
=> Non c' è niente che si possa mangiare. (Non c' è niente che possa essere mangiato.)
There is nothing to eat.
=> There is nothing that could be eaten. (There is nothing that can be eaten.)
Actually this type of sentence corresponds to a sentence in passive voice but has nothing to do with the construction we already know.
The construction is similar to this one, which we have already seen.
È un problema da risolvere. => È un problema che si deve risolvere.
This problem is to be resolved.
But this construction is not only another way to form the passive voice, it expresses obligation as well, what is not the case in the construction we have seen before (Niente da mangiare.)
da to describe characteristics
It doesn' t matter what language you have as your mother tongue, Spanish, English, French, German etc. it is more or less sure that you are going to be caught in that trap, because any other language except Italian uses with in this circumstances.
A child with blond hair.
Un enfant avec les cheveux blonds.
Un niño con cabellos rubios.
Ein Kind mit blonden Haaren.
But in Italian we use da and not con in this context.
La bella dai capelli d'oro.
The beauty with the golden hair.
Il gigante dai piedi d'argilla.
The giant with fictile feet.
Il giovane dagli occhi blu profondi iniziò a girare per casa scoprendo cose nuove che non aveva mai visto.
The boy with the deep blue eyes started to walk around the house and discovered things he had never seen bevor.
Un pesce dalla bocca grande.
A fish with a big mouth.
Il medico dal naso rosso che guarisce con le risate.
A medecin with a red nose, who cures with laughter.
But if the characteristic is not inherent, for example in the case of clothes there is clear preference for con.
La donna col cappello verde.
The woman with the green hat.
La donna con la gonna in Afganistan è una specie di sacrilegio.
A woman with a skirt is considered a blasphemie in Afghanistan.
In singular cases you can find exemples where an inherent characteristic as added with di.
Un ragazzo di soli 16 anni modifica un pickup trasformandolo in auto elettrica.
A sixteen year old boy modified a pickup and converted it into a electric car.