Když prší, beru si s sebou deštník i do knihovny.

Czech doesn’t use a dummy subject like English it for weather.

• pršet = “to rain” is an impersonal verb.
• You just say Prší. = “It’s raining.” (literally “Rains.”)
• So Když prší literally is “When rains”, but it’s the normal way to say “When it rains”.

You almost never add a subject like to (“it”) here; To prší sounds wrong in standard Czech.

This sentence describes a general habit:

• Když prší – “When it rains” (whenever that happens)
• beru si – present tense of an imperfective verb, used here for something repeated or usual.

So the natural English sense is:
“When it rains, I (usually) take an umbrella with me, even to the library.”

For one specific future situation, you’d normally change the verbs (see next question).

You’d normally use a future time clause and a perfective verb in the main clause:

• Když bude pršet, vezmu si s sebou deštník do knihovny.
  = “When it rains / when it is raining, I will take an umbrella with me to the library.”

Structure:

• bude pršet – future of “to rain”
• vezmu si – perfective (vzít si) = “I’ll take (once, as a single act)”

The verb here is really the reflexive verb brát si:

• brát = “to take, to be taking (in general)”
• brát si něco = “to take something for oneself / to take something with oneself”

So:

• Beru deštník. – “I take the umbrella.” (neutral, can be OK e.g. in some contexts)
• Beru si deštník. – “I take an umbrella (for myself/to have it with me).”

In the meaning “I take an umbrella with me”, brát si (with si) is the usual, natural verb.

They do two different jobs:

• si belongs to the verb brát si = “to take for oneself / take along”.
• s sebou literally = “with oneself”.

The phrase brát si něco s sebou is a very common fixed combination meaning:

• “to take something (along) with you”

So:

• Beru si deštník. – “I (habitually) take an umbrella (for myself).”
• Beru si s sebou deštník. – “I (habitually) take an umbrella with me.”

In many contexts s sebou can be omitted without changing the meaning much, but including it makes the “with me” part explicit.

i here means “even / also”, and its position shows what is being emphasized.

In … beru si s sebou deštník i do knihovny, the focus is:

• “I take an umbrella with me, even to the library.”

That suggests the library is a place where you might normally not bother with an umbrella, but even there you take it.

Compare:

• … beru si s sebou i deštník do knihovny.
  → “I even take an umbrella with me to the library.”
  (emphasis more on umbrella as an extra thing you also take)
• … beru si s sebou deštník i do školy, i do knihovny.
  → “I take an umbrella with me both to school and to the library.”

So i attaches to what follows it and highlights that element (“even/too/as well”).

The preposition do (“to, into”) requires the genitive case.

The noun knihovna (“library”) is a regular feminine -a noun:

Singular:

• nominative (dictionary form): knihovna
• genitive: knihovny

After do you need genitive, so:

• do knihovny = “to the library”

do knihovna is ungrammatical; the ending must change to show the case.

Here knihovny is genitive singular of knihovna.

• Preposition do (meaning physical or abstract “into / to”) is always followed by genitive.
• The genitive often appears after prepositions of movement into / towards a place.

So:

• jdu do knihovny – “I’m going to the library.”
• jdu do školy – “I’m going to school.”
• jdu do práce – “I’m going to work.”

All those nouns are in the genitive after do.

They differ in both preposition and case, and therefore in meaning:

• do knihovny – “to the library” (movement towards/into the library)
  
  • do
    • genitive (knihovny)
• v knihovně – “in the library” (location inside the library)
  
  • v
    • locative (knihovně)

So:

• Beru si s sebou deštník do knihovny.
  = I take the umbrella to the library (when I go there).
• Mám s sebou deštník v knihovně.
  = I have the umbrella in the library (while I’m there).

Because když prší is a subordinate clause (“when it rains”), and Czech spelling rules require a comma between a subordinate clause and the main clause.

Pattern:

• [Subordinate clause], [main clause].

So:

• Když prší, beru si s sebou deštník i do knihovny.
• Když mám čas, chodím do knihovny. – “When I have time, I go to the library.”

If the order is reversed, you still write the comma:

• Beru si s sebou deštník i do knihovny, když prší.

You can say it, but it sounds more formal or bookish:

• Při dešti beru s sebou deštník.
  literally “During rain I take an umbrella with me.”

Nuances:

• Když prší – the normal, everyday way: “when it rains”.
• Při dešti – “in case of rain / during rain”; more formal, often used in written instructions, notices, or more literary style.

In casual speech about your habits, Když prší, beru si s sebou deštník… is much more natural.

Yes, deštník is the normal everyday word for a rain umbrella.

A few basics:

• Gender: masculine inanimate.
  
  • sg: deštník, deštníku, deštníku, deštník, dešníku, deštníkem
  • pl: deštníky, deštníků, deštníkům, deštníky, deštnících, deštníky
• Example:
  
  • Mám deštník. – I have an umbrella.
  • Bez deštníku nejdu. – I’m not going without an umbrella.

There is also paraple, a bit old‑fashioned/colloquial and sometimes humorous, but deštník is the safe, neutral choice.