The Hanafi school was founded by Abu Hanifa. He was born in Iraq in about 700. The Hanafi school can be described this way:
Broad-minded without being lax, this school appeals to reason (personal judgment) and a quest for the better. It is generally tolerant and the largest movement within Islam. The Hanafi school is known for its liberal religious orientation that elevates belief over practice and is tolerant of differences within Muslim communities.
The Maliki school was found by Malik ibn Anas. He lived from 710-795:
This school recorded the Medina consensus of opinion, and uses hadith (tradition) as a guide. The Maleki is predominant in north, central and west Africa and Egypt. Following the tradition of Imam Malik, this school appeals to "common utility...the idea of the common good."
Malik did not record the fundamental principles on which he based his school and on whose basis he derived his judgments and to which he limited himself in the derivation of his rulings. In that respect he resembled his contemporary, Abu Hanifa, but not his student, ash-Shafi'i, who did record the principles he used in derivation and defined them precisely, specifying the motives which moved him to consider them and their position in deduction.
The Shafi'i school was begun by Muhammad ibn Idris al-Shafi'i. He lived from 767-819:
According to the Shafi'i school the paramount sources of legal authority are the Qur'an and the Sunnah. Of less authority are the Ijma' of the community and thought of scholars (Ijitihad) exercised through qiyas. The scholar must interpret the ambiguous passages of the Qur'an according to the consensus of the Muslims, and if there is no consensus, according to qiyas.
The Hanbali school was founded by Ahmad bin Hanbal (died in 855) and is the smallest of the four schools:
It derives its decrees from the Qur'an and the Sunnah, which it places above all forms of consensus, opinion or inference. The school accepts as authoritative an opinion given by a Companion of the Prophet, providing there is no disagreement with another Companion. In the case of such disagreement, the opinion of the Companion nearest to that of the Qur'an or the Sunnah will prevail.
The Wahhabi sect is part of the Hanbali school. Al-Wahhabi was born in around 1700. His initial goal was to rid the Muslim Bedouin of Sufi practices; his efforts grew into an attempt to return Islam to its original state- basically a Muslim reformer similar to Calvin or Luther.
The most obvious example of Wahhabi practice is in Saudi Arabia:
To the Wahhabis, for example, performance of prayer that is punctual, ritually correct, and communally performed not only is urged but publicly required of men. Consumption of wine is forbidden to the believer because wine is literally forbidden in the Quran. Under the Wahhabis, however, the ban extended to all intoxicating drinks and other stimulants, including tobacco. Modest dress is prescribed for both men and women in accordance with the Quran, but the Wahhabis specify the type of clothing that should be worn, especially by women, and forbid the wearing of silk and gold, although the latter ban has been enforced only sporadically. Music and dancing have also been forbidden by the Wahhabis at times, as have loud laughter and demonstrative weeping, particularly at funerals.Another site with links to good information about Islam is The Sunnah: Practice and Law.
The Wahhabi emphasis on conformity makes of external appearance and behavior a visible expression of inward faith. Therefore, whether one conforms in dress, in prayer, or in a host of other activities becomes a public statement of whether one is a true Muslim. Because adherence to the true faith is demonstrable in tangible ways, the Muslim community can visibly judge the quality of a person's faith by observing that person's actions. In this sense, public opinion becomes a regulator of individual behavior. Therefore, within the Wahhabi community, which is striving to be the collective embodiment of God's laws, it is the responsibility of each Muslim to look after the behavior of his neighbor and to admonish him if he goes astray.