How do beliefs and values inspire people?

The question is very broad because beliefs and values are two different things. Beliefs can inspire people to do many things. Including go against a person's values based on the belief that it is for the greater good, or that the end justifies the means. Values are a mixture of internal conscience and learned acceptance from life experiences. Therefore, people are inspired to follow their values to make their life fit with what they would find to be valuable or, in a Word, "good".

Values can change, but people are born with a sense of values that are pretty universal and are usually so widely intertwined with society, that the basic values do not change. However, upbringing, trauma, greed, and many other variables can often distort someone's values or even desensitize them completely.

Beliefs are more of a choice. Beliefs can change when something we thought was right, no longer seems right or doesn't fit with what we feel is right. Beliefs are based on a scale of faith and logic. Some beliefs are very extreme in one way or another. A belief based solely on faith can sometimes be considered irrational be those that base their beliefs more on logic. However, there are many who try to find a middle path between the two extremes.