Na stole je další vlas.

Word by word:

• Na = on
• stole = table in the form used after na for location
• je = is
• další = another, an additional, sometimes next
• vlas = hair as a single hair / strand of hair

So the sentence is literally:

On the table is another hair.

In natural English, that is usually:

There is another hair on the table.

Because na can take different cases depending on meaning:

• na + accusative = movement onto something
• na + locative = location on something

Here, the hair is already located on the table, so Czech uses the locative:

• stůl = table
• na stole = on the table

Compare:

• Položil vlas na stůl. = He put the hair onto the table.
• Vlas je na stole. = The hair is on the table.

Because Czech nouns change form depending on case.

The dictionary form is:

• stůl = table

But after na when it means location, stůl goes into the locative singular:

• na stole = on the table

This is just the normal declension pattern of stůl. The vowel also changes a bit:

• stůl
• stole

That kind of stem change is common in Czech.

Czech usually does not need a separate word for English there in existential sentences.

English says:

• There is another hair on the table.

Czech simply says:

• Na stole je další vlas.

The verb je means is, and the sentence structure itself expresses the idea there is.

So in many cases, English there is / there are is just Czech je / jsou.

Here další means another or an additional.

So:

• další vlas = another hair
• je další vlas = there is another hair

Depending on context, další can also mean:

• next
• further
• additional

For example:

• další den = the next day
• další otázka = another / next question

In this sentence, another is the most natural translation.

Good question. Czech vlas means one individual hair, one strand.

• vlas = a hair
• vlasy = hairs / hair

In English, hair is often uncountable when talking about someone’s hairstyle or hair in general:

• She has long hair.

But when talking about a single strand, English can use a hair:

• There is a hair in my soup.

That is exactly the kind of meaning Czech vlas has here: one visible individual hair.

Because Czech does not have articles like English a, an, and the.

So Czech often expresses meaning without an article:

• vlas can mean a hair or the hair, depending on context

In this sentence, další vlas naturally means another hair even though there is no separate word for a.

Context does the work that articles do in English.

Yes. Další is an adjective-like word, so it agrees with the noun in:

• gender
• number
• case

Here:

• vlas is masculine singular nominative
• so další is also in masculine singular nominative

In this particular form, další looks the same for several genders, so the agreement is not very visible. But it is still there grammatically.

Both are possible, but they have slightly different emphasis.

• Na stole je další vlas.
  This sounds like: On the table, there is another hair.
  It presents the location first and then introduces what is there.

• Další vlas je na stole.
  This sounds more like: Another hair is on the table.
  It focuses more on the hair as the topic.

Czech word order is more flexible than English, and it often reflects information structure:

• known/background information first
• new or important information later

So if you are looking at the table and noticing things on it, Na stole je další vlas is very natural.

Yes. By itself, it is simply a neutral statement:

• There is another hair on the table.

But in real life, the tone can make it sound like:

• an observation
• a complaint
• annoyance
• surprise

For example, if someone is cleaning and finds yet another hair, další can carry the sense of yet another.

Czech does not change the grammar here; the feeling mostly comes from context and intonation.

A rough pronunciation guide:

• Na = nah
• stole = approximately STO-leh
• je = yeh
• další = approximately DAL-shee
• vlas = vlahs

A few notes:

• j in Czech is pronounced like English y
• š is like English sh
• á is a long vowel
• Czech r is usually trilled or tapped

So roughly:

nah STO-leh yeh DAL-shee vlahs

If you want to say There are more hairs on the table, you would use plural:

• Na stole jsou další vlasy.

Changes:

• je → jsou = are
• vlas → vlasy = hairs / hair

But note the nuance:

• další vlas = another single hair
• další vlasy = additional hairs / more hairs

If you mean visible strands on a surface, plural is fine.