When A does something to B we can express it in two different ways. For example, Johnny, the mechanic, painted my car, so Johnny is A and my car is B:

1-    Talking about A:    Johnny painted my car in black      (active voice)
2-    Talking about B:    My car was painted in black       (passive voice)

As you can see, the object of the active sentence becomes the subject of the passive sentence. In examples 1 and 2 we are talking about the same event, but in 1 we are talking about Johnny, what he did, and in 2 we are talking about my car, what they did to it. So we use a passive voice when we want to talk about what happened to someone or something. Another example:

-    Your son broke my window (I’m talking about what your son did)
-    My window was broken yesterday (I’m talking about what happened to my window)

The subject from the active sentence usually disappears in the passive voice, as in the examples above, but if it is important to mention the subject, you can do it using the preposition BY (we call that “the agent” of the passive sentence):

-    Dalí painted that picture in 1967   (Dalí= subject)
-    That picture was painted by Dalí in 1967   (Dalí= agent)

You can also notice a change in the verb form. The active verb becomes a passive verb (broke was broken). To change an active verb into a passive form simply use the verb To Be in the same tense, and then add the past participle of that verb.

-    I use your computer (present) your computer is used by me (present + p.p.)
-    I will use your computer (future) your computer will be used by me (future + p.p.)
-    I have used your computer (present pft.) your computer has been used by me (present pft. + p.p.)

So to change an active sentence into a passive sentence the changes are these:

Timmy washed the dog The dog was washed (by Timmy)

USE

The passive voice is mostly used when we want to talk about an event, but are not interested in who or what caused it.

     Obama was elected president of the United States in 2008

We are talking about Obama. American voters elected Obama, but we don’t want to talk about the voters, we want to talk about Obama, so we use a passive voice and we don’t mention the voters. Let’s see examples of other cases when we don’t want to mention the performer of the action:

when we don't know it
    He has been killed   
(you would never say "by someone" or "by them" or “by a killer” because it doesn't give any information at all)

when it is obvious
    He has been arrested  (of course, by the police)
    You will be fired   (of course, by your boss)

when it has already been mentioned
    The firemen arrived at once and the fire was extinguished   (by the firemen)

when you don't want to make it known
    The original documents have been destroyed

when people in general are the agents
    Wine can be bought in a supermarket

NOTE: In this last case there is an alternative active construction with "you", "they" or "one" (more formal) as impersonal subject.
    You can buy wine in a supermarket
    They have built a new hospital in Salisbury
    One can never find a taxi when one needs it

MENTIONING THE AGENT

So in a passive sentence we don’t usually mention the agent, but we do when we think it gives important information.

     This book was written by my brother

We are not talking about my brother; we are talking about this book, so we need a passive voice. Nevertheless, a very important fact about this book is that my brother wrote it. In fact, that is probably why we are talking about this book. So in this case we use a passive voice but we mention the agent. Other examples:

    The new bridge was inaugurated by the king
    A dog was bitten by a man in Piccadilly
    All the problems were caused by your wife

When the agent expresses the instrument or the means, not the performer, we usually use WITH instead of BY

    Water filled the room The room was filled with water   (not by water)
    A bomb killed him He was killed with a bomb