Pričvrsti dasku ekserom i čekićem.

It is the imperative form, meaning a command: attach / fasten.

More specifically:

• it is 2nd person singular
• it is used when speaking to one person informally
• the implied subject is ti

So the sentence is addressing one person directly: Attach the board...

Because dasku is the accusative singular form of daska.

• daska = nominative singular, the dictionary form
• dasku = accusative singular, used for the direct object

In this sentence, the board is the thing being fastened, so it must be in the accusative.

They are in the instrumental singular.

The instrumental case is often used to show the tool, means, or instrument used to do something. Here it means:

• ekserom = with a nail / using a nail
• čekićem = with a hammer / using a hammer

So Serbian uses the instrumental where English uses with.

Both are instrumental singular, but Serbian nouns do not all take exactly the same ending.

• ekser → ekserom
• čekić → čekićem

A useful rule of thumb is:

• many nouns take -om
• after certain softer or palatal consonants, -em is common

Since čekić ends in ć, it takes -em: čekićem.

Pričvrsti comes from a perfective verb.

That matters because perfective verbs usually focus on a completed result. In this sentence, the goal is that the board ends up attached. That is why the perfective is natural.

In instructions and commands, Serbian very often uses the perfective when the speaker wants the action to be carried through to completion.

Because Serbian does not have articles like English.

So dasku can mean:

• a board
• the board

Which one is meant depends on context. The same is true for ekserom and čekićem:

• with a nail and a hammer
• with the nail and the hammer

English must choose an article, but Serbian usually leaves that unstated.

Yes, but that is completely normal in Serbian.

The subject ti is understood from the imperative form pričvrsti, so Serbian does not need to say it explicitly.

If you did say ti, it would usually add emphasis:

• Ti pričvrsti dasku...

But in ordinary instructions, the pronoun is normally omitted.

You would use pričvrstite instead of pričvrsti:

Pričvrstite dasku ekserom i čekićem.

That form can mean:

• speaking to several people
• speaking to one person formally

So:

• pričvrsti = singular informal
• pričvrstite = plural or formal

Yes. Serbian word order is fairly flexible because the cases show what each word is doing.

This sentence begins with the verb because that sounds natural for an instruction:

• Pričvrsti dasku ekserom i čekićem.

But other orders are possible, for example:

• Dasku pričvrsti ekserom i čekićem.

That would put more emphasis on dasku. Even when the order changes, the cases still show:

• dasku = object
• ekserom i čekićem = instruments

No. I simply means and.

In ekserom i čekićem, both nouns are in the instrumental because both are part of the same with / using phrase.

So:

• ekserom = instrumental
• čekićem = instrumental
• i just links them

No. Another common word is čavao.

Both can mean nail, but usage can vary by region, style, and habit:

• ekser is very common in everyday speech in many places
• čavao is also standard and widely understood

So a learner may encounter both.

That is a very common question, especially because čekićem contains both sounds.

• č is a harder sound, somewhat like ch in church
• ć is a softer sound, with no exact English equivalent

In čekićem:

• the first letter č is the harder sound
• the ć near the end is softer

Also:

• č and ć are different letters in Serbian
• confusing them can change pronunciation and sometimes meaning

For many English speakers, hearing and producing the difference takes practice.