Among the many stereotypes said about Islam is that Islamic governments are autocratic. It's clear that anyone who believes such a stereotype has never heard of the Caliphs, or has never read about Islam and its history. Let's put that aside and take a look at how Allah teaches us democracy in the right ways.
Shura in the Qur'an
Aya 38 of the 42nd Sura of the Qur'an, called Shura:
Aya 159 of the 3rd Sura of the Qur'an, called Al-Imran:
Those who hearken to their Lord, and establish regular Prayer; who (conduct) their affairs by mutual consultation; who spend out of what We bestow on them for Sustenance.
Shura and the Caliphate
And by the Mercy of Allah, you dealt with them gently. And had you (Prophet Muhammad P.B.U.H.) been severe and harsh-hearted, they would have broken away from about you; so pass over (their faults), and ask (Allah's) Forgiveness for them; and consult them in the affairs. Then when you have taken a decision, put your trust in Allah, certainly, Allah loves those who put their trust (in Him).
Known as Shura, democracy in the Qur'an is what we know now as representative democracy. The first four Caliphs were selected by Shura, which is similar to election, but only the wise and trustworthy are involved in the decision. After the Four Rightly-Guided Caliphs, the later Caliphs had less democracy. During the Islamic Golden Age, the Caliphs rised to power through inheritance and might, but the decisions were made by Shura.
The Muslim counselors advised submission to rulers as long as they were Muslims but also stressed the duty of the ruler to rule by shura. They based this recommendation on the passages from the Qur’an mentioned above. The verses indicate that shura is praiseworthy but do not indicate who should be consulted, what they should be consulted about, or whether the ruler or the shura should prevail in the event the two do not agree.
Modern Practices of Shura
Nowadays, Arab countries do not practice Shura as much as before. There is, though, a Shura Council, in which representatives of different parts of the nation are involved in the decision made. However, the ultimate power lays within the hands of the ruler. This is not the righteous way of ruling by Islamic Shari'a and by the teachings of the Qur'an. This is why Arab countries are not in their best states. I mean what's better than ruling by the Islamic Shari'a - the Islamic law that Allah teaches us?
[Source] Credit goes to Sukran from Truth Booth Online for making such a wonderful research, which is actually much larger than this. Please refer back to his page for a more detailed explanation.