Само собой: short for само собой разумеется – it goes without saying
So you open up the morning newspaper, armed with four years of Russian grammar and conversation classes, three years of studying Russian literature in the original, and two years of watching Russian videos on YouTube. You're prepared.
And then you read: Спасибо за митинг на Сахарова. Thank you for the rally on… Well, that can't be right. If the rally is on something, you need the prepositional case: на Сахарове. Sheesh. Editorial standards are going down the drain … unless I've got it wrong. Maybe it's the accusative case and the author is thankful that the rally moved toward …? That doesn't make sense. What's going on here?
What's going on is simple: a word was left out – проспект (avenue). Спасибо за митинг на проспекте Сахарова (Thank you for the rally on Sakharov Prospekt.)
When stating an address or place, in colloquial speech — and apparently now in the written language — Russians often leave out the place marker words, like улица (street), площадь (square), переулок (lane), or станция метро (metro station). But they keep the name of the street, square, or metro station in the grammatical case it would be in if the word was there. So instead of saying: Повернись на улицу Комсомола (Turn on Komsomol Street), they say: Повернись на Комсомола (Turn on Komsomol).
Sometimes they leave out more than one place marker. In St. Petersburg, you might be told: Выходи на Ленина (Get off at Lenin), which is super-short for Выходи на станции "Площадь Ленина" (Get out at the Lenin Square station).
This might be a snap for native speakers, but it's hard for us non-natives to maintain grammatical cases determined by omitted words. It's slightly easier to get right when the street or station name is an adjective, although you have to remember what gender noun it modifies. Езжайте до конца Кутузовского (Drive to the end of Kutuzovksy [Prospekt].) Идёшь налево на Фрунзенскую (You turn left on Frunzenskaya [Embankment].)
In general, as Russians chat away, they leave out a lot of words. They chop off the longer bits of set expressions, so that само собой разумеется (it goes without saying) is само собой. Sometimes they only quote half of a saying or proverb: Ну, век живи … (Well, live and … ) You can complete the phrase: Век учись (Learn). Or you can just nod sagely.
Nodding sagely is a good technique when you have no idea what proverb is being quoted.
Most of all, it seems, Russians eschew verbs. This is good news for those of us who haven't mastered all those conjugations or the finer points of aspect. Instead of saying, Ты что говоришь? (What are you talking about?), you can say: Ты что? Instead of asking, Кому положить добавки? (Who can I serve seconds to?), you can say: Кому добавки?
Conversations are often retold in verbless shorthand. Он мне — Дура! А я ему — Сам дурак! (He told me, "You're an idiot," and I said, "No, you're the idiot.")
Once you get the hang of this, you can have an entire conversation without a single verb being uttered.
Ты куда? (Ты куда идёшь? Where are you going?)
К соседям. (Пойду к соседям. I'm going to the neighbors.)
Я – в магазин. (Я иду в магазин. I'm going to the store.)
А твоя мама? (А что будет делать твоя мама? What about your mother?)
Со мной. (Она идёт со мной. She's coming with me.)
Sure beats conjugation.