K večeři potřebujeme dvě lžíce, dvě vidličky a jeden nůž.

The preposition k takes the dative case, so večeře changes to večeři.

• dictionary form: večeře = dinner
• after k: k večeři

In this kind of sentence, k večeři is an idiomatic way to say for dinner or with dinner.

You will often see the same pattern with other meals:

• k snídani = for breakfast
• k obědu = for lunch
• k večeři = for dinner

Czech often drops subject pronouns when they are not needed, because the verb ending already shows who is doing the action.

Here, potřebujeme means we need, so my is unnecessary.

• potřebujeme = we need
• my potřebujeme = we need (with extra emphasis or contrast)

So the sentence is completely natural without my.

Potřebujeme is the 1st person plural present tense form of potřebovat = to need.

So:

• potřebuji = I need
• potřebuješ = you need
• potřebuje = he/she/it needs
• potřebujeme = we need

In this sentence, it simply means we need.

They are in the accusative case, because they are the direct objects of potřebujeme.

We are asking: What do we need? Answer: two spoons, two forks, and one knife.

So:

• potřebujeme co? = what do we need?
• dvě lžíce, dvě vidličky a jeden nůž

In this sentence, the accusative forms happen to look the same as the nominative forms for these nouns.

Because dvě is the form of two used with feminine and neuter nouns.

• lžíce is feminine
• vidlička is feminine

So you get:

• dvě lžíce
• dvě vidličky

With a masculine noun, you would usually use dva instead:

• dva stoly = two tables

This is one of the first places where Czech numerals show gender agreement.

Because nůž is a masculine noun, so the numeral one must agree with it.

The basic forms of one are:

• jeden for masculine
• jedna for feminine
• jedno for neuter

So:

• jeden nůž = one knife
• jedna vidlička = one fork
• jedno jablko = one apple

Here nůž is masculine inanimate, so jeden nůž is correct.

Here it is plural.

This is confusing because the noun lžíce has a form that looks the same in:

• nominative singular: lžíce = spoon
• nominative/accusative plural: lžíce = spoons

But in this sentence, dvě lžíce must be plural, because dvě means two.

Compare:

• jednu lžíci = one spoon
• dvě lžíce = two spoons

So the phrase is definitely plural, even though the form may look familiar from the singular dictionary form.

Because after the numerals 2, 3, and 4, Czech normally uses the nominative/accusative plural form of the noun.

So:

• dvě lžíce = two spoons
• tři lžíce = three spoons
• čtyři lžíce = four spoons

But from 5 onward, Czech usually switches to the genitive plural:

• pět lžic = five spoons

The same pattern applies to vidlička:

• dvě vidličky
• tři vidličky
• čtyři vidličky
• pět vidliček

Yes, you could also say Potřebujeme k večeři dvě lžíce, dvě vidličky a jeden nůž.

Czech word order is more flexible than English word order. The version in your sentence puts k večeři first, which gives it a kind of topic-setting role: As for dinner / for dinner, we need...

Very roughly:

• K večeři potřebujeme... = For dinner, we need...
• Potřebujeme k večeři... = We need for dinner...

Both are grammatical. The difference is mainly about focus and information structure, not basic meaning.

Yes. K večeři is a very common Czech phrase, and its exact English translation depends on context.

It can mean:

• for dinner
• at dinner
• to have for dinner
• with dinner

For example:

• Co bude k večeři? = What’s for dinner?
• Dáme si rybu k večeři. = We’ll have fish for dinner.

In your sentence, because the objects are spoons, forks, and a knife, the meaning is clearly something like for dinner / for the dinner setting.

Here are the main ones:

• č = like ch in church
• ž = like the s in measure
• ř = a special Czech sound; roughly like a rolled or trilled r mixed with ž
• ů = a long oo sound, like in food
• í = a long ee sound, like in see

Approximate pronunciations:

• lžíce ≈ lzhee-tseh
• vidličky ≈ vid-lich-kee
• nůž ≈ noozh
• večeři ≈ veh-cheh-rzhi
  (This is only approximate; ř does not have a perfect English equivalent.)

For many English speakers, ř is the hardest sound in the whole sentence.