El geocacher firma el libro de registro.

Because Spanish usually uses a definite or indefinite article before a singular countable noun when you are talking about a specific person or thing.

Here, el geocacher means the geocacher — a particular geocacher, not just any one.

Spanish does this more regularly than English:

• el geocacher = the geocacher
• un geocacher = a geocacher

It is basically a borrowed word from English, and people who do geocaching often use it as-is. In everyday usage, especially in hobby communities, that is quite common.

You may also come across alternatives depending on the speaker or context, but geocacher is understandable and natural in geocaching contexts.

In this sentence, it behaves like a regular masculine singular noun:

• el geocacher
• los geocachers

Because firma is the conjugated verb, while firmar is the infinitive.

• firmar = to sign
• firma = he/she signs or you sign (formal usted)

In El geocacher firma el libro de registro, the subject is el geocacher, which is third person singular, so the verb must be firma.

A quick comparison:

• Yo firmo = I sign
• Tú firmas = you sign
• Él/ella firma = he/she signs

Yes. Firma can be either:

• a noun: signature
• a verb form of firmar: he/she signs

In this sentence, it is clearly a verb because it comes after the subject:

• El geocacher firma... = The geocacher signs...

If it were a noun, the structure would look different, for example:

• La firma del geocacher = The geocacher’s signature

Because libro is also a singular masculine noun, and here it refers to a specific logbook.

So:

• el libro = the book
• el libro de registro = the logbook / the record book

Spanish normally keeps the article with the noun, just as English does here.

Literally, it means something like book of record/registration.

This is a very common Spanish pattern:

• noun + de + noun

The second noun tells you what kind of first noun it is.

Examples:

• libro de cocina = cookbook
• mesa de madera = wooden table
• libro de registro = logbook / register book

So de registro describes the purpose of the book.

Spanish does not normally use ’s possession the way English does. Instead, it often uses:

• de = of
• or a definite article plus context

So instead of something like the register’s book, Spanish says:

• libro de registro = book of record / logbook

And instead of the geocacher’s signature, Spanish would usually say:

• la firma del geocacher

Yes. It is in the simple present: firma.

In Spanish, the simple present can cover several ideas depending on context:

• a habitual action: The geocacher signs the logbook
• a general action: The geocacher signs the logbook
• sometimes even what English might express as is signing

If you specifically want to emphasize is signing right now, Spanish often uses:

• El geocacher está firmando el libro de registro.

But the simple present sentence is perfectly normal.

Because the basic unmarked Spanish word order is the same as English here:

subject + verb + object

• El geocacher = subject
• firma = verb
• el libro de registro = direct object

So the structure is very straightforward.

Spanish can change word order more easily than English for emphasis, but this version is the most neutral and natural.

Because firmar is a transitive verb here: someone signs something.

So:

• who signs? el geocacher
• what does he sign? el libro de registro

That makes el libro de registro the direct object.

There is no personal a here because the object is a thing, not a person.

Because the personal a in Spanish is generally used before specific human beings, and sometimes pets or personified beings, when they are direct objects.

Here, el libro de registro is a thing, so no a is used.

Compare:

• El geocacher firma el libro de registro. = The geocacher signs the logbook.
• El geocacher ve al dueño. = The geocacher sees the owner.

In the second sentence, al dueño refers to a person, so the a appears.

In this phrase, registro means something like record, register, or log. It is the normal word in many standard expressions.

So libro de registro is a natural Spanish way to say logbook or register book.

You do not need to translate each word too literally. It is best to learn the whole phrase as a chunk:

• firmar el libro de registro = to sign the logbook

Yes, especially in a geocaching context. A speaker in Spain would understand it without any problem.

That said, depending on context, people might also say shorter or more specialized alternatives if everyone already knows they are talking about a cache log:

• firmar el log
• firmar el cuaderno
• firmar el registro

But El geocacher firma el libro de registro is clear, grammatical, and natural enough.