What were the religious differences between the Samaritans and Jews? How did the Samaritans worship God differently?

The one continuing and neutraly describable major point of difference between Jews and Samaritans is that the Jews believe that the one center of the religion must be on mount Moriah in Jerusalem (the Temple mount), while the Samaritans believe that the one center must be on mount Gerizim (in the Shomron region -- West Bank).

Other than that --

Jewish materials from the Roman period generaly consider the Samaritans ignorant of the details of many required practices, though at the same time the Jewish sages praise the dedication of the Samaritans in those instances where the Samaritans are knowledgeable.

Thus -- two instances - Jewish sages held that the Samaritans were not learned in issues of Temple sacrifice purity -- and therefore required caution in associating with them where this could become an issue. But on the other hand, they praised the Samaritan dedication and skill at prayer -- and therefore counted Samaritans for the purpose of a Minyan (prayer quorum).

Another quite major issue is that by Jewish understanding, the Samaritans do not properly follow the laws of marriage, divorce, and inheritance. This means that a Jew can not marry a Samaritan due to questions regarding the "legitimacy" of the birth of the potential spouse.

This probably works in both directions -- and the Samaritans may have concerns over the "legitimacy" of a potential spouse who is Jewish.

A very big difficulty and concern for Jews in the Roman period with respect to the Samaritans was that the Jews of the time believed that the Samaritans worship a bird on Gerizim as an incarnation or at least symbol of God. This would be prohibited under the Jewish understanding of idolatry.

http://www.gotquestions.org/Samaritans.html