The usage is similar to 把 (ba) sentences, but 被 is a marker of passive voice in Chinese. Some example sentences:
他的钱包被偷走了。His wallet was stolen (literally "stolen and gone away with").
他被妈妈骂了一顿。He was scolded by his mother.
There are also other markers of passive voice in Chinese, most notably 让 and 叫, which are basically interchangeable with 被. But direct usage of a verb after a passive marker (omitting the agent) is only possible with 被. The 被 character in the second sentence 他被妈妈骂了一顿。could be replaced with 让 or 叫, but such replacement is not be possible in the first sentence 他的钱包被偷走了。since the agent is omitted here and the verb is used directly after the passive marker.
Usage of negative and other adverbs, like 不,没,应该,别 etc., is similar to 把 sentences - they are placed directly before 被 or other passive marker. Some examples:
他的手机没让人拿走。His cellphone was NOT taken away by anyone.
他没被老师批评。He was NOT scolded by the teacher.
Sometimes 给 is added between the agent and the verb:
他又被哥哥给打了。He was beaten by the older brother again.
他的雨伞被人给拿走了。His umbrella was taken away by someone.
给 does not have any specific meaning here, but the sentences sound more colloquial this way.
Hope this helps.