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.

Why use them? 
Passive sentences are used for several main reasons:
1. To indicate that one has been negatively affected.
2. To shift emphasis from the "doer" of the action to the one affected by that action.
3. To avoid having to mention the "doer" of the action, either because it is unknown, or for other reasons.

How to use them 
Normal use of 被 has a few preconditions:
1. The verb to be used with 被 needs to have an object (this will become the new subject of the 被 sentence). Verbs that take objects are called transitive verbs.
2. If you're going to state who the verb was done by (the "doer"), then the subject doing the original action must be known.
3. The verb can't be too simple (for example, a one-character verb like 吃). Put simply, something needs to come after the verb. That "something" can be a particle, a complement, or sometimes even an additional object.

Forming a 被 Sentence
Let's use our example above to show how the process works:

In this sentence, "the boy" is the subject. The verb is 吃, "to eat," but it needs something else after it, which is 了 in this case. The object is 热狗, "the hot dog."

This sentence meets all the preconditions. Now all you need to do is introduce the preposition 被 and move the parts of the sentence around a bit:
1. The object is 热狗. Move that to the front; it's the new subject in the 被 sentence.
2. Add 被 after the subject, then insert what was previously the subject. (It's now the doer.)
3. Finish off with the verb phrase 吃了. (Don't forget to include the part that comes after the verb!)
So the new 被 sentence is:
Rè ɡǒu bèi nán hái chī le.
热狗 被 男孩 吃 了 。The hot dog was eaten by the boy.

subject+被+doer+verb phrase

Forming a 被 Sentence with No "Doer"

If we want to, we can also omit the "doer" (男孩) and say:
Rè ɡǒu bèi chī le.
热狗 被 吃 了 。The hot dog was eaten.

subject+被+verb phrase

Forming a Negative 被 Sentence

There's just one other complication. What if you want to make a sentence in the negative? For example, continuing with our wonderful theme, if you wanted to say:

The hot dog was not eaten by the boy.

In this case, the negative adverb 没有 needs to be inserted before the 被[2], and the verb still needs something after it, which in this case is 掉. (We're using 掉, which adds a meaning of "totally" to the verb, because you don't use 了 when you use 没有 to negate.) This is what we get:

subject+没有+被+doer+verb phrase

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