Capital letters

In the Russian language every new sentence begins with a capital letter. Any word begins with a capital letter after full stop, ellipsis, question and exclamation marks which end a sentence.

Наступила весна. По улицам гуляет теплый ветер, звенит капель. – It's spring. Soft breeze strolls through the streets, drip-drop tinkle.
Неужели вы пришли? Наконец-то! – Have you really come? Finally!
Я и забыл, как вы прекрасны... Рад вас видеть. – I've forgotten how beautiful you are... Glad to see you.

Direct speech begins with a capital letter after a narrative comment, so do quotations.
Отец вошел в комнату и сказал: "Сегодня едем за город". – Father entered the room and said: "Today we are going to the country".

First name, second name and patronymic name also begin with a capital letter.
Нашего директора зовут Петров Иван Васильевич. – Our chief's name is Petrov Ivan Vasil'yevich.

Pet's names (cat's, dog's, bird's, horse's etc).
Полкан, Найда (собаки). Мурка, Барсик (кошки). – Polkun, Nayda (dog's). Murka, Barsik (cat's).

Names related to religion and mythology.
Иисус Христос, Будда, Тор, Беовульф – Iesus Christus, Buddha, Thor, Beowulf.

Names of artworks.
Венера Милосская, Джоконда, Постоянство памяти. – The Venus de Milo, La Gioconda,
The Persistence of Memory.

Names of fictitious beings, heroes and fictional characters.
Дед Мороз и Снегурочка, Колобок и Лиса. – Santa Clause and The Snow Maiden, Roly-Poly and The Fox.

Names of astronomical and any geographical objects.
Astronomical objects: Солнце – the Sun, Земля – the Earth, Марс – the Mars, Луна – the Moon.
Continents: Евразия – Eurasia, Северная Америка – North America, Антарктида – Antarctica.
Countries: Соединенные Штаты Америки – the United States of America, Португалия – Portugal, Франция – France.
Districts, regions, states: Калифорния – California, Ленинградская область – Leningrad Region, Хоккайдо – Hokkaido.
Cities: Нижний Новгород – Nizhniy Novgorod, Милан – Milan, Оттава – Ottawa, Лас-Вегас – Las Vegas.
Mountains and ranges: Эверест – Everest, Альпы – the Alps.
Oceans, seas, rivers and lakes: Тихий – the Pacific Ocean, Атлантический – the Atlantic Ocean, Амазонка – Amazon River, Байкал – Lake Baikal.
Streets, alleyway, highways and other parts of urban infrastructure: улица Ленина – Lenina street, Волоколамское шоссе – Volokolamskoye highway.

Holidays' names.
Новый год – New Year, Первое мая (или 1 Мая) – May Day, Рождество Христово – Christmas, Масленица – Cheese Fare Week.

Organizations' and establishments' names.
Министерство культуры – Ministry of Cultural Affairs, Тюменская целлюлозно-бумажная фабрика – Tyumen pulp and paper factory.

Books', newspapers' and broadcasts' titles.
"Аргументы и факты" – "Argumenty i Fakty", "Преступление и наказание" – "Crime and Punishment", "Время" – "Vremya".

Brands' and signs' names.
Найк – Nike, Шевроле – Chevrolet, Лада – Lada.

Attention! We write all pronouns with a lowercase letter if they don’t denote any above mentioned cases.
Друг попросил меня помочь с заданием, и я согласился. – My friend had asked me for help with a task, so I agreed.

Names of languages and nationalities are also with a small letter.
В силу особенностей произношения итальянцам русский язык дается проще, чем французский - нам, русским. – It is easier for Italians to learn the Russian language because of the pronunciation's peculiarities. But we, Russians, have difficulties with French.

Probably, you have noticed that sometimes Russians write the names of months and days in English with a lowercase letter. The point is that there is also this "lowercase letter rule" in Russian.

понедельник - Monday, вторник - Tuesday, среда - Wednesday; январь - January, март - March, сентябрь - Septermber.