What it does#
The prepositional (предложный падеж) is the only case that never stands alone. It always follows a preposition, which is exactly where its name comes from. Its two everyday jobs are location (where something is) and the topic of speech or thought (what something is about).
Я живу в Москве.
I live in Moscow.
Книга на столе.
The book is on the table.
Мы говорим о музыке.
We're talking about music.
The endings#
The prepositional is the most regular case of all: almost everything ends in -е. There's one important exception to memorise and one small group of "locative" nouns.
- стол
- столе
- masculine → -е
- книга
- книге
- feminine -а → -е
- окно
- окне
- neuter -о → -е
- море
- море
- neuter -е unchanged
- лекция
- лекции
- -ия → -ии
- здание
- здании
- -ие → -ии
- дверь
- двери
- feminine -ь → -и
- стол
- столах
- -ах
- книга
- книгах
- -ах
- окно
- окнах
- -ах
- словарь
- словарях
- -ях
- море
- морях
- -ях

Where you use it#
1. Location: with в and на answering где? (where?): в школе, на столе.
2. Topic: with о (about): говорить о книге, думать о будущем.
3. Circumstance: with при (in the presence of / at the time of): при Петре Первом.
Студенты сидят на лекции.
The students are at the lecture.
Расскажи мне о фильме.
Tell me about the film.
Грибы растут в лесу.
Mushrooms grow in the forest.

Location vs. direction#
The same prepositions в and на take two different cases depending on meaning. Location (где?) → prepositional; direction toward (куда?) → accusative. This pair is worth drilling until it's automatic:
Я в школе.
I'm at school. (location, prepositional)
Я иду в школу.
I'm going to school. (direction, accusative)
Same preposition, opposite endings: в школе → в школу. With the prepositional done, just the instrumental remains. The cases overview ties all six together.
Common mistakes#
Putting -е on -ия / -ие nouns. These take -ии: it's на лекции and в здании, never лекцие / здание.
Confusing location with direction. Use the prepositional for being somewhere (я в школе), the accusative for going somewhere (я иду в школу). Leaving a noun in -е when you mean motion is the classic slip.
Using -е for the locative nouns. A handful of masculines take a stressed -у for location: в лесу, not в лесе.