El geocaching empieza cuando buscamos el geocaché.

Because geocaching is being used as a noun, meaning the activity or sport itself, and in Spanish general activities are often introduced with the definite article.

So El geocaching empieza... is like saying Geocaching begins...

This is very common in Spanish:

• El fútbol es popular.
• La natación es buena para la salud.

English often drops the in these cases, but Spanish often keeps it.

Because the subject is el geocaching, which is third person singular, so the verb has to match it.

The infinitive is empezar = to begin / to start.

Its present tense forms include:

• yo empiezo = I begin
• tú empiezas = you begin
• él/ella empieza = he/she/it begins

Since el geocaching is treated like it, Spanish uses empieza.

Also, empezar is a stem-changing verb, so e changes to ie in most present-tense forms:

• empezar → empieza
• empezar → empiezan

But:

• nosotros empezamos
• vosotros empezáis

Buscamos is the nosotros form of buscar in the present tense.

So:

• busco = I look for
• buscas = you look for
• busca = he/she looks for
• buscamos = we look for

In this sentence, buscamos means we look for / we search for.

Spanish often uses the simple present where English might use either:

• we look for
• we are looking for

The exact translation depends on context, but here the simple present fits well.

Because the sentence is expressing a general idea or a typical situation.

El geocaching empieza cuando buscamos el geocaché means something like a general truth: the activity begins at the moment we start searching for the cache.

Spanish commonly uses the present tense for this kind of statement:

• La clase empieza cuando llega el profesor.
• La película empieza cuando apagan las luces.

It is not describing one specific past event, but a general pattern.

Because this sentence is talking about something understood as real, general, or habitual.

After cuando, Spanish uses:

• the indicative for habitual, general, or known actions
• the subjunctive for future or not-yet-real actions in some contexts

Here, cuando buscamos describes a general situation, so the indicative is correct.

Compare:

• El geocaching empieza cuando buscamos el geocaché.
  General/habitual idea.
• Empezará cuando busquemos el geocaché.
  Future idea; now the action is still not realized, so busquemos is subjunctive.

Because buscar normally takes a direct object in Spanish, with no extra preposition.

So Spanish says:

• buscar el libro
• buscar las llaves
• buscar el geocaché

English often uses look for, but Spanish does not need a separate word for for here.

So:

• buscar = to look for not
• to look
  • separate word for for

That is why buscar por is not the normal structure here.

The accent mark shows where the stress falls: ge-o-ca-CHÉ.

In adapted Spanish spelling, the accent helps show that the final syllable is stressed. Without the accent, a Spanish speaker might naturally stress it differently.

This word is a borrowing, and you may also see variation in real life:

• geocaché
• geocache

But in a fully Spanish-style spelling, geocaché makes the pronunciation clearer.

Yes, in this sentence it is treated as masculine: el geocaché.

Many borrowed nouns in Spanish are assigned a grammatical gender, and masculine is often the default, especially for newer or less settled loanwords.

So here:

• el geocaché = the geocache

Even if a learner cannot always predict the gender of every loanword, the important thing is to learn the article together with the noun:

• el geocaché

Yes. Comenzar and empezar both mean to begin / to start, and in many contexts they are interchangeable.

So you could also say:

• El geocaching comienza cuando buscamos el geocaché.

In everyday speech, empezar is extremely common and often feels a bit more conversational, but both are correct.

Not by itself in standard modern Spanish. In this sentence, buscamos is present tense: we look for / we are looking for.

To say we searched for, Spanish would normally use a past tense, such as:

• buscamos only in certain varieties or older narrative contexts can create ambiguity, but for learners, it is safest to read it here as present.
• more clearly: buscamos el geocaché ayer may be interpreted as preterite in speech depending on context and accentless writing, because the nosotros form of some -ar verbs is identical in present and preterite.

That is an important point:

• buscamos can mean we look for
• buscamos can also mean we looked for

The tense is determined by context.

In your sentence, because of the general meaning, it is clearly present.

A rough pronunciation guide is:

el he-o-ka-ching em-pee-etha kwan-do boos-ka-mos el he-o-ka-CHE

For Spain specifically:

• ge usually sounds like a strong English h sound: he
• z in empieza is pronounced like th in thin in most of Spain
• ch is like English ch
• the stress in geocaché is on the last syllable: -ché

A more natural connected pronunciation would be something like:

el heokaching empietha cuando buscamos el heokaché