Breakdown of Я сейчас иду в библиотеку.
я
I
сейчас
now
в
in / to (direction)
идти
to go (on foot) / to proceed, go (of a process)
Questions & Answers about Я сейчас иду в библиотеку.
Why does the word for library end in -у (библиотеку) instead of -а (библиотека)?
Because it is the destination of your movement. When you are going to a place, feminine nouns that normally end in -а change their ending to -у. This is the Accusative case. If you were just saying "This is a library," you would use the dictionary form: библиотека.
Why use в here instead of на for the word "to"?
For destinations, you use в (into) for enclosed spaces and buildings. Since a library is a building you go inside, we say в библиотеку. You use на (onto) for open spaces, islands, or events (like going to a concert or to work).
Does иду mean I am walking or driving to the library?
It means you are going on foot. The dictionary form is идти, and its "I" form иду is specifically for moving by your own two feet. If you were driving or taking a bus, you would use a different verb (еду). Using иду also implies you are making an active, one-way trip right now.
Does сейчас have to go right after Я?
Not necessarily! Russian word order is very flexible. Placing сейчас right before the verb is just a very natural way to emphasize that the action is happening right at this moment. Moving it to the beginning or end of the sentence is also perfectly fine and would mean the same thing.