The Conjunctions ЧТО and ЧТОБЫ
Russian has two conjunctions, что and чтобы, which resemble one another but which have radically different functions. The first is a simple verb complement marker requiring the indicative mood, while the second has two specialized meanings, one of which requires the conditional. The conditional is associated with the particle бы, which we see in чтобы, and the past tense of the verb, which чтобы sometimes requires (see below).
The Conjunction Что "(that)"
Perhaps the most common of the Russian subordinating conjunctions is the ubiquitous что. This conjunction marks a verbal complement, i.e. a sentence that functions as a direct object of a verb. For example, if you have a word for what you wish to express as a direct object, you simply put that word in the accusative case: Максим слышал музыку 'Maxim heard the music'. But what if there is no word for what Maxim heard. In that case you have to describe what he heard in a sentence. However, sentences cannot reflect case and direct objects must have case in Russian. So, in Russian you have to put in a 'dummy' pronoun to reflect case and the most common one is что: Максим слышал, что Горький произвёл скандал в Нью Йорке 'Maxim heard (that) Gorky created a scandal in New York'. Notice that the corresponding 'that' in English is omissible; in Russian it is not.
Ельцин сказал, что экономика растёт. Yeltsin said (that) the economy is growing. Я надеюсь, что Ельцин прав. I hope (that) Yeltsin is right. Валя забыл, что пистолет заряжён Valya forgot (that) the gun was loaded. Я думаю, что Валя виноват. I think (that) Valya is at fault.
(Для того) чтобы "(in order) to"
The conjunction чтобы (or для того, чтобы) basically means "in order to" in English, e.g. I came downstairs (in order) to kiss the baby. However, it is also used in the same sense as to or for . . . to when to introduces a subordinate clause, indicating what it is that someone wants someone else to do, e.g. Mama wants Lara to clean up her room. To in this sentence might seem like an infinitive marker, but it translates in Russian as a subordinating conjunction.
The important thing to remember is that чтобы requires the past tense of the verb if the subject of the subordinate verb is different from that of the main verb: Мама хочет, чтобы Лара убрала комнату. The literal translation would be something like "Mama wants that Lara should clean up her room", acceptable in some dialects of New York English, no doubt, because so many Russians and East Europeans immigrated there. If the subjects of the verbs in the main and subordinate clauses is identical, the subordinate verb is an infinitive: я спустился вниз (для того,) чтобы поцеловать ребёнка "I came down the stairs (in order) to kiss the baby."
Here are a few examples to peruse. Read them over carefully, comparing them with the translations and noting the various meanings of чтобы and how it translates into English.
"In order to" "For . . . to" Он приехал в Москву, чтобы пожениться. Мама сказала, чтобы ты вынесла мусор. He came to Moscow (in order) to get married. Mama said for you to take out the garbage. Юлия читает газету, чтобы стать умнее. Саша хочет, чтобы мы забрали его. Julia reads the newspaper (in order) to get smarter. Sasha wants us to pick him up.
Now you try your hand at it.