In Iran, the supreme leader is the highest figure. I want to know, what is the relationship between him and the president. Does the president need the nod of supreme leader every time he makes a decision? if so, why do people in Iran always blame the government for incorrect policy? They dare not?
The role of the Supreme Leader is spelled out in Chapter VIII of the Iranian constitution (unofficial English translation).
The SL controls the president in the way that he* has large influence on deciding who can run for president in the first place. Any presidential candidate needs to be accepted by the guardian council, and six of its twelve members are chosen by the SL.
The SL is officially above the President and has far-fetching but mostly indirect rights. He controls the military and appoints many other important positions in the government. Among them is also half of the aforementioned Guardian Council which reviews all laws and can reject them for violating the constitution or the Islamic law. There is not much the SL decides directly, but his de facto influence is still very strong because he can instantly fire a lot of important people when they make decisions he doesn't agree with.
However, the president is not among those the SL can fire at will. The SL can try to impeach the president, but needs a two third majority of the assembly (parliament) to do so.
The duties delegated to the president are in Chapter IX of the Iranian constitution. Things the president can do without having to consult the SL are:
- sign international treaties
- plan the fiscal budget
- state employment affairs (those which are not made by the SL)
- appoint ambassadors
- sign laws which were decided upon by the assembly (but sill need to pass the GC)
In these ways, the Iranian president is an executive leader while the legislative power is in the hands of the parliament.
Regarding the Iranian public "not daring" to criticize the Supreme Leader and blame the secular government instead: The SL is also the religious leader of Iran and Iran is still a quite fundamentalist state. Criticizing the SL can easily be interpreted as criticizing Islam as a whole. Apostasy is punished by the Revolutionary Guard which is also under direct control of the SL. So people need to treat lightly in this regard.
However, you did not specify for which "incorrect policies" people blame the government instead of the clergy. It's not unlikely you actually are talking about things which indeed are in the hands of the elected president and parliament.
* Considering that we are talking about an Islamic religious position here I believe I can forego using gender-neutral pronouns. I might have to do some research to find out if it might be theoretically possible for the SL to be a woman, but I think we can all agree that Iran isn't so far yet that a female SL is a realistic possibility.