El salero está junto al pimentero, así que no tienes que buscarlos por toda la mesa.

Because the sentence is talking about location: where the salt shaker is.

In Spanish, estar is usually used for location:

• El salero está junto al pimentero. = The salt shaker is next to the pepper shaker.

By contrast, ser is used more for identity, description, origin, and similar ideas:

• El salero es de cristal. = The salt shaker is made of glass.

So here, está is the natural choice because it tells you where something is.

Junto a means next to, beside, or right by.

So:

• junto al pimentero = next to the pepper shaker

The al is a contraction:

• a + el = al

So:

• junto a el pimentero → junto al pimentero

This contraction is mandatory in standard Spanish whenever a is followed by the article el.

Así que is a very common linking expression meaning so, therefore, or which means that.

In this sentence:

• El salero está junto al pimentero, así que...
• The salt shaker is next to the pepper shaker, so...

It introduces the consequence of the first idea:

• since they are together, you do not need to search for them.

It is best learned as a set phrase rather than translating it word by word.

Tener que + infinitive means to have to + verb.

So:

• tienes que buscarlos = you have to look for them

With no, it becomes:

• no tienes que buscarlos = you do not have to look for them

Important point: this usually means lack of necessity, not prohibition.

So here it means:

• you don’t need to look for them

If you wanted to say you must not look for them, Spanish would usually use something else, such as:

• no debes buscarlos
• no puedes buscarlos depending on the exact meaning.

Because -los means them, referring to the two objects already mentioned:

• el salero
• el pimentero

So:

• buscar = to look for
• buscarlos = to look for them

Spanish often attaches object pronouns to an infinitive:

• tienes que buscarlos

You could also say:

• no los tienes que buscar

Both are grammatically correct. In this sentence, attaching the pronoun to the infinitive sounds very natural.

Because it refers to two masculine nouns:

• el salero
• el pimentero

When Spanish refers back to masculine plural nouns, it uses los:

• buscarlos = to look for them

Even if there were one masculine noun and one feminine noun together, Spanish would still normally use the masculine plural:

• masculine + feminine = los

So in this sentence, los is exactly what you would expect.

Here por means something like around, all over, or throughout.

So:

• buscarlos por toda la mesa = to look for them all over the table

And toda la mesa means the whole table.

Together, the idea is:

• you do not need to search all around the table to find them

This use of por is very common when talking about movement through an area or searching in different parts of a place.

Spanish uses definite articles more often than English does.

In this sentence, the speaker is talking about specific, known objects in the situation:

• the salt shaker
• the pepper shaker
• the table

Even if English might sometimes sound more flexible depending on context, Spanish very naturally uses the articles here:

• El salero está junto al pimentero...

This is one of those areas where Spanish often sounds more definite than English.

Yes. A very common alternative is:

• al lado del pimentero = next to the pepper shaker

So you could also say:

• El salero está al lado del pimentero.

Both are natural.
Junto a can sound slightly more direct or compact, while al lado de is also extremely common in everyday speech.

Because the sentence is talking to one person: you singular.

• no tienes que buscarlos = you do not have to look for them

If the speaker were talking to more than one person in Spain, it would normally be:

• no tenéis que buscarlos

That is the vosotros form, which is standard in Spain.