Bei Sentences, which are called 被字句 (bèizìjù) in Chinese, are a key way to express the passive in modern Mandarin Chinese. In passive sentences, the object of an action becomes the subject of the sentence, and what would have been the subject of the normal (active voice) sentence, the "doer" of the action, becomes secondary, and may or may not be included in the passive sentence.

被 sentences (被字句 in Chinese) are simply sentences which use a passive verb and the preposition 被. 被 sentences are not the only way to create the passive verb form in Chinese, but they are the most common, and definitely the type to tackle first.

For the sake of clarity, let's give some examples of the passive in English first:

1. The boy ate the hot dog. (normal sentence in the active voice; note that "the hot dog" is the object of the verb "ate")
2. The hot dog was eaten by the boy. (the same sentence in the passive voice; "the hot dog" is now the subject, and "the boy" is the "doer")
3. The hot dog was eaten. (also in the passive voice, but with the "doer" omitted)

Now let's see those same sentences in Chinese:

Adding Adverbs in a 被 Sentence 
What if you want to include adverbs in your 被 sentence? wher should those go? They go in the same place as the negative adverb 没有, above. (Frequently you'll see the word "adverbial" or "adverbial adjunct" used in this case, because some words in Chinese, such as time words, act like adverbs but are technically nouns.) In the following example we'll use the adverb 刚, which is used to express that something just recently happened.
subject+adverb+被+doer+verb phrase

Advanced modern usage 
In recent years, special uses of 被 have popped up online. These uses occur with verbs which don't normally ever use 被, in order to emphasize a lack of control over the action, often including some kind of foul play or underlying statistical falsification.

Examples include: