Wa`alaykum as-salamu wa rahmatullahi wa barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear brother in Islam, thank you for your question, which reflects your desire to have a clear view of the teachings of Islam. Allah commands Muslims to refer to scholars to become well acquainted with the teachings of Islam in aspects of life.
Muslims believe that pluralism and political freedom are intrinsic parts of Islamic teachings. It is worth stressing here that we accept the articles and principles of democracy that agree with the teachings of Islam and reject those principles that are un-Islamic.
In his response to your question, Sheikh Muhammad Al-Mukhtar Ash-Shinqiti, director of the Islamic Center of South Plains in Lubbock, Texas, states the following:
Democracy consists of a set of values and procedures. One of most the important values of democracy is people's right to choose their leader and not to be ruled by force or tyranny. This is also an Islamic value, which we call shura or mutual consultation.
Another important value is checks and balances by which powers are distributed and separated in a way that achieves independence of each power and the ability to check and correct each other. In Qur'anic terminology, this is called al-mudafa`ah, which is a very important Islamic concept that protects the society against corruption. Almighty Allah says, [Had not Allah checked one set of people by means of another, the earth would indeed be full of mischief] (Al-Baqarah 2:251).
As for the procedures of democracy, such as elections, voting, campaigning, et cetera, these are means for achieving principles. In this sense, democracy is also an Islamic principle. This does not mean that each democratic country is Islamic, but it does mean that each Islamic country should be democratic.
As for non-Muslim countries applying democracy, they are still non-Muslim. In one way, they adopt an Islamic political system, but they also lack other aspects of Islam such as belief, manners, and social conduct.