To stop typically can be translated as
smettere and
fermare. There are of course other possible translations, but I'll concentrate on these two, which are the most common and also the most commonly mixed up. As it is impossible to single out a rule that categorically says when you should use one or the other, the best thing to do is provide some examples of usage, which will show that
smettere tends to be used in a more generic and abstract manner than
fermare:
SmettereDevi smettere di fumare
You must stop smokingMi stai dando fastidio, smettila! (smettila here is a generic request to stop doing something)
You are annoying me, stop it!Ha appena smesso di piovere
It has just stopped rainingSmetto di fare questo lavoro se non mi danno un aumento
I’ll stop doing this job if they don’t give me a riseFermare
Ferma la macchina, voglio scendere
Stop the car, I want to get out
Ferma la registrazione
Stop the recordingFermarsi (reflexive)
Fermati, mi stai facendo male
Stop it, you are hurting myself (I’m asking you to physically stop what you are doing)
Fermatevi a dormire a casa nostra
Stop to sleep at our house (we can put you up for the night)