Depuis, pendant and pour are prepositions. They express the duration of an event and can all be translated as "for" in English. You will learn below how and when to use each of them.
Depuis (since, for) is used to talk about an action that began in the past and is continuing in the present. It is used with the present tense (as opposed to the past or progressive past in English).
J'étudie le francais depuis trois ans.
I have studied French for three years.
NOTE: In the example above, I have started studying French three years ago and I am still studying French now.
Depuis is also used to talk about an action that was occurring in the past before being interrupted. In that instance, the imperfect is used, followed by the perfect tense (as opposed to the past perfect progressive followed by the simple past in English).
Je lisais un roman depuis trois heures quand tu es arrivé.
I had been reading a novel for three hours when you arrived.
You could also use the less formal phrase Ça fait... que instead of depuis:
Ça fait une heure que j'attends. I have been waiting for an hour.
Ça faisait une heure que j'attendais. I had been waiting for an hour.
Pendant (during, for) is used to talk about the entire duration of an action. It can be used in the present (when describing a habit), in the past (when it is no longer the case) or in the future.
Je joue au tennis pendant une heure tous les jeudis.
I play tennis for an hour every Thursdays.
Nous allons vivre en France pendant trois ans.
We are going to live in France for three years.
NOTE: When pendant is followed by a noun, it is a synonym of durant
j'ai appris le français pendant/ durant mon séjour.
I learnt French during my trip.
Pour (for) also expresses an entire duration but can only be used to refer to a future event.
Elle va habiter en France pour trois ans.
She is going to live in France for three years.
NOTE that pour can always be replaced with pendant, but pendant cannot always be replaced with pour.
There are cases where the present tense can be used with pour but only when the present is used to refer to a future action.
Je vais en France pour trois ans.
I am going to France for three years.
In the example above, the present tense is used to describe an action that is imminent/ about to happen.
There is a difference between depuis and depuis que.
Depuis que is used to introduce a subordinate clause (rather than a nominal phrase).
For example you would say:
J'étudie le français depuis la rentrée universitaire.
But you would say:
J'étudie le français depuis que j'ai commencé l'université.
NOTE that the subordinate clause does not have to be in the present tense.
The same applies to pendant and pendant que.