Quote Originally Posted by Wyrm
So in a lot of time the "они" is omitted from the sentences? If this is the case, how would I know when to use a plural verb without any subject when I am supposed to fill in the blank (missing the verb, of course).
Well, in a sloppily constructed exercise this might be a problem. But, as Оля pointed out, it isn't as big a deal as it might seem initially.

Этот город строили пять лет. (Impersonal. They had been building this city for five years.)
Этот город строился пять лет. (Imperfective passive. City was built for five years, but it wasn't completed.)
Этот город был построен за пять лет. (Perfective passive. City was built in five years.)
Neither is much like the variant with impersonal "They", if you know where to look and have an infinitive to insert. (unusual reflexion or auxiliary "to be" used with the passive participle.)

Potentially pseudogrammatical gibberish of someone who studied all this more than fifteen years ago follows: What is and what isn't "true" passive in Russian is somewhat of a gray area. The strictest definition requires use of participle, but reflexion is used like that all the time, mainly with imperfective verbs. In fact passive participles of imperfective verbs as in "делан, строен" sound archaic and uneducated. Perfective "сделан, построен" sound OK, and are used. In fact using reflexion instead would mean that a city indeed built itself. "Город построился за пять лет".

Imperative is a bit trickier, with no verb the only clue is usually the word order:
plural imperative:
Стройте этот город ещё пять лет! (Build this city for five more years!)
Singular imperative:
Строй этот город ещё пять лет! (Build this city for five more years!)



Quote Originally Posted by Wyrm
Secondly, is this only true with "они" or is it also true with "он, она," etc.?
Except for the cases above and some rare and "literary" constructions, pronouns always are dropped only if they're otherwise obvious from the context. So, a proper exercise should contain some clue as to what pronoun was there before the drop.

One of those literary constructions that doesn't obey these rules, and which you may find sometimes, is dropped "ты".

It's like impersonal "man", "one" or "you". And again, it's used mostly in the literature, so if your main interest is spoken language you may ignore it.

From "The Hound of the Baskervilles":
"Yes, it is an interesting instance of a throwback, which appears
to be both physical and spiritual. A study of family portraits is
enough to convert a man to the doctrine of reincarnation. The
fellow is a Baskerville--that is evident."
Compare:
Да, любопытный пример возврата к прошлому и в физическим и в
духовном отношении. Вот так начнешь изучать фамильные портреты и, пожалуй,
уверуешь в переселение душ. Он тоже Баскервиль, это совершенно очевидно.