Die hardloopskoen is nuut.

Die means the.

A useful thing to remember is that Afrikaans uses die for both singular and plural definite nouns:

• die hardloopskoen = the running shoe
• die hardloopskoene = the running shoes

So unlike English, it does not change.

It is capitalized only because it is the first word of the sentence.

In the middle of a sentence, it would normally be lowercase:

• Ek sien die hardloopskoen. = I see the running shoe.

Afrikaans usually writes compound nouns as a single word.

So:

• hardloop = run / jogging / running
• skoen = shoe
• hardloopskoen = running shoe

English sometimes separates compounds more often, but Afrikaans strongly prefers joining them into one word.

Hardloop is the verb to run or to jog.

Inside the compound hardloopskoen, it describes the kind of shoe: a shoe used for running.

So it works a bit like English running in running shoe.

Because this is a full sentence with the verb is:

• Die hardloopskoen is nuut. = The running shoe is new.

Here, nuut is a predicate adjective, so it comes after is.

If you put the adjective before the noun, you get a noun phrase instead:

• die nuwe hardloopskoen = the new running shoe

That is not the same structure as The running shoe is new.

Afrikaans adjectives often have different forms depending on position.

• After a linking verb like is, you usually use the basic form: nuut
• Before a noun, you usually use the attributive form: nuwe

Compare:

• Die hardloopskoen is nuut. = The running shoe is new.
• Die nuwe hardloopskoen = The new running shoe

So nuut and nuwe are forms of the same adjective.

Yes, but it is even simpler than in English.

Afrikaans uses is for all persons and numbers in the present tense:

• Ek is = I am
• Jy is = you are
• Hy is = he is
• Ons is = we are
• Hulle is = they are

So Afrikaans does not switch between am / is / are the way English does.

Hardloopskoen is singular: running shoe.

The plural is hardloopskoene: running shoes.

So the plural sentence would be:

• Die hardloopskoene is nuut. = The running shoes are new.

Notice that Afrikaans still uses is, even with a plural subject.

You normally use the Afrikaans double nie pattern:

• Die hardloopskoen is nie nuut nie. = The running shoe is not new.

In simple terms:

• the first nie goes after the verb phrase
• the second nie goes at the end of the clause

This is a very common Afrikaans pattern.

Yes.

• 'n hardloopskoen = a running shoe
• die hardloopskoen = the running shoe

So you could say:

• 'n Hardloopskoen is nuut. = A running shoe is new.

A small spelling point: 'n stays lowercase even at the beginning of a sentence, so the next word gets the capital letter.