The present infinitive form of verbs is used much more in the Italian language than in English. First a few examples of similar constructions, then all the different uses.
Similar Usage in both Languages:
1. After modal verbs and sapere when it means 'know how to'
Dobbiamo studiare = we have to study
Non possono venire = they are not able to come
So cucinare = I know how to cook
Vorrei andare in Italia = I would like to go to Italy
2. After many impersonal verbs and expressions
Che bello essere qua = how nice it is to be here
Bisogna riprovare = you need to try again
È importante studiare = it's important to study
È difficile capirlo = it's hard to understand him
3. After 'da' where English often, but not always, uses the infinitive as well
Ho molto da fare = I have a lot to do
Lucca è una città da vedere = Lucca is a city worth seeing
Hai un appartamento da affittare? = Do you have an apartment to rent?
Non c'era da preoccuparsi = there was nothing to worry about
Vuoi qualcosa da bere? = do you want something to drink?
Different Usage in Italian
1. After prepositions and conjunctions where English uses the gerund (ing)
È partito senza salutarci = he left without saying goodbye
Oltre a visitare Lucca = besides visiting Lucca
Invece di mangiare a casa = instead of eating at home
Prima di uscire = before going out
Piuttosto che prendere la macchina, usa la bici = rather than taking the car, use the bike
2. After verbs of emotion where English often uses the gerund
Preferisco stare a casa stasera = I prefer staying at home this evening
Ti dispiace cucinare oggi? = do you mind cooking today?
Non m'interessa imparare l'Italiano = I'm not interested in learning Italian
Non vale la pena farlo = it's not worth doing
3. After 'fare' and 'lasciare' (far fare will be covered in a separate article)
Ti faccio sapere = I'll let you know
Fammi vedere = let me see/show me
Mi ha fatto arrabbiare = he made me angry
Lascia perdere = let it go
Lascia stare = drop it
Ho lasciato passare il camion = I let the truck overtake
Lasciami finire il lavoro = let me finish my work
4. At the beginning of emphatic statements, also where English often uses the gerund
Noleggiare una macchina in Italia è semplice = renting a car in Italy is easy
Guidare a Napoli è pericoloso = driving in Naples is dangerous
Vivere con una donna italiana è complicato = living with an Italian woman is complicated
5. After verbs of opinion and belief where the subject is the same and therefore Italian uses the present infinitive after 'di' not the subjunctive after 'che'
Penso di venire più tardi = I think I'll come later
Non credo di poter venire = I don't think I can come
Crede di avere un raffreddore = he thinks he's got a cold
Loro hanno paura di prendere l'aereo = they're afraid of flying
6. Exclamations where English sometimes uses the gerund
Ciro essere puntuale? Quando mai? = Ciro being on time? When has that ever happened!
Io vivere in Francia? Assolutamente no! = me living in France? No way!
Perdonarlo? Mai! = forgive him? Never!
7. As a noun
Lamentarsi non serve a niente = complaining is useless
Col passare del tempo il dolore si attenua = as time passes the pain eases
Non sopportava l'abbaiare del cane = he couldn't stand the dog barking
8. When forming the negative imperative in the 2nd personal singular
Non dimenticare le chiavi = don't forget the keys
Non fare casino stasera = don't go crazy/let it get out of hand this evening
Non andarci = don't go there
Non correre = don't run
9. As an imperative/instruction
Tirare = pull
Soffriggere le patate = fry the potatoes
Spingere = push