Jeśli znajdziesz jakąś starą półkę albo regał, też mi się przyda w nowym pokoju.

Because Polish often drops subject pronouns when the verb ending already makes the subject clear.

• znajdziesz = you will find / you find
• it is 2nd person singular

So Jeśli znajdziesz... already means If you find....
You could add ty, but that would usually sound emphatic: Jeśli ty znajdziesz...

Znajdziesz is from the perfective verb znaleźć = to find.

In Polish, perfective verbs do not normally have a true present meaning. Their present-looking forms often refer to the future. So:

• znajdziesz = you will find
• Jeśli znajdziesz... = If you find...

This is very natural after jeśli when talking about a future possibility.

Jeśli means if.

Yes, jeżeli is also possible. The difference is mostly stylistic:

• jeśli = very common, neutral, everyday
• jeżeli = a bit more formal or careful

In this sentence, jeśli sounds completely natural.

It is accusative singular feminine, because półkę is the direct object of znajdziesz.

Base forms:

• jakaś → jakąś
• stara → starą
• półka → półkę

All three words agree with each other in gender, number, and case.

So:

• jakąś = some
• starą = old
• półkę = shelf in the accusative

Jakąś is the accusative feminine singular form of jakaś, which means some.

In this sentence it gives an indefinite meaning, like:

• some old shelf
• any old shelf, depending on context

It makes the sentence sound non-specific: the speaker does not mean one particular shelf.

Grammatically, starą agrees directly only with półkę, because półka is feminine.

But in meaning, listeners will often understand it as applying to the whole alternative: an old shelf or bookcase.

If you want to say it fully and explicitly for both nouns, you could repeat the words:

• jakąś starą półkę albo jakiś stary regał

The original version is shorter and natural in conversation.

They are related, but not the same:

• półka = shelf
  usually one shelf, or a wall shelf
• regał = bookcase / shelving unit / set of shelves

So the speaker is saying that either a single shelf or a larger shelving unit would be useful.

Both albo and lub can mean or.

The main difference is style:

• albo = more common in everyday speech
• lub = a bit more formal or bookish

So półkę albo regał sounds very natural in conversation.

Because the sentence means one or the other, not both together.

• półkę albo regał = a shelf or a bookcase
• the idea is: if you find either one, it will be useful

So the verb is singular:

• przyda się = it will come in handy

If the sentence used and, you would expect a plural verb:

• półka i regał mi się przydadzą

The verb here is przydać się komuś, which means:

• to be useful to someone
• to come in handy
• to be of use

So mi się przyda means:

• it will be useful to me
• I’ll be able to use it
• it’ll come in handy for me

A very literal breakdown is:

• mi = to me
• się przyda = will prove useful / will come in handy

Because przydać się is the normal dictionary form of this verb expression.

In other words, się is not optional here. You learn it as one unit:

• przydać się komuś = to come in handy to someone

Without się, you would have a different verb and a different meaning.

Mi is the normal short, unstressed dative form of I / me in the middle of a sentence.

• mi = common, neutral, unstressed
• mnie = fuller form, often used for emphasis, contrast, or after prepositions

So here:

• też mi się przyda = natural

If you said też mnie się przyda, that would sound wrong.
A more emphatic structure with mnie would need a different arrangement, and even then mi is what you normally expect here.

Because w means in, and when it refers to location, it takes the locative case.

Base forms:

• nowy → nowym
• pokój → pokoju

So:

• w nowym pokoju = in the new room

This is a very common pattern:

• w domu
• w mieście
• w pokoju

Też means also / too.

It suggests some previous context, for example that other things have already been mentioned, and this item would be useful as well.

So:

• też mi się przyda = that would also come in handy for me

Its position is natural because Polish word order is flexible, and adverbs like też often move depending on what the speaker wants to emphasize.

Because Jeśli znajdziesz jakąś starą półkę albo regał is a subordinate clause introduced by jeśli.

In standard Polish punctuation, such clauses are separated by a comma from the main clause:

• Jeśli znajdziesz..., też mi się przyda...

So the comma is required here.