Der Reservierungsbeleg liegt hier.

Because Reservierungsbeleg is a masculine noun in German, so its basic singular article is der.

In this sentence, it is also the subject, so it appears in the nominative case:

• der Reservierungsbeleg

A good habit with German nouns is to learn the noun and article together:

• der Reservierungsbeleg

It is in the nominative case because it is the subject of the sentence.

The subject is the thing that is in the state described by the verb. Here, the reservation slip/document is the thing that lies / is located here.

So:

• der Reservierungsbeleg = nominative subject
• liegt = finite verb
• hier = adverb of place

German often prefers a position verb when talking about where something is located.

Here, liegen means something like:

• to be lying
• to be located lying down
• for many objects, simply to be

So Der Reservierungsbeleg liegt hier is more natural and specific than just Der Reservierungsbeleg ist hier.

A useful comparison:

• Das Buch liegt auf dem Tisch. = The book is on the table.
• Die Flasche steht auf dem Tisch. = The bottle is on the table.

German often chooses:

• liegen for things that are lying flat or not upright
• stehen for things that are upright
• sitzen for people/animals, and sometimes objects fitted into place

This is a very common learner question.

• liegen = to be lying, to be located lying down
• legen = to lay, to put something down

So:

• liegen describes a state
• legen describes an action

Examples:

• Der Beleg liegt hier. = The receipt is lying here.
• Ich lege den Beleg hierhin. = I put the receipt here.

Also notice:

• liegen does not take a direct object
• legen does take a direct object

It is a compound noun, which is very common in German.

It is made of:

• Reservierung = reservation
• s = a linking sound/letter, often called a linking s
• Beleg = receipt, voucher, document, slip

So Reservierungsbeleg is literally something like:

• reservation document
• reservation receipt
• reservation slip

In German compounds, the last part is the main noun. So this word is a kind of Beleg.

That also explains the gender:

• der Beleg
• therefore der Reservierungsbeleg

That s is a linking s. In German, compounds sometimes insert an s between the parts.

So:

• Reservierung
  • Beleg becomes
• Reservierungsbeleg

This does not always happen in every compound, and there is not always a simple rule you can predict perfectly. Often it just has to be learned as part of the word.

You will see the same kind of linking element in many other compounds.

Because in a normal main clause, German follows the verb-second rule.

In this sentence:

• Der Reservierungsbeleg = first element
• liegt = second element
• hier = the rest

So the structure is:

• Subject + verb + adverb

This is one of the most important word-order rules in German main clauses.

Yes, absolutely.

That version is also correct:

• Hier liegt der Reservierungsbeleg.

German lets you move another element into the first position for emphasis or style. But the finite verb still stays in second position.

Compare:

• Der Reservierungsbeleg liegt hier. = neutral, starting with the subject
• Hier liegt der Reservierungsbeleg. = emphasis on location, here

Both are natural.

Hier is an adverb of place. It means here and tells you where the reservation document is.

It does not change form:

• hier stays hier

It can appear in different positions depending on emphasis:

• Der Reservierungsbeleg liegt hier.
• Hier liegt der Reservierungsbeleg.

The plural is:

• die Reservierungsbelege

So you could say:

• Die Reservierungsbelege liegen hier.

Notice the changes:

• article: der → die
• noun: Reservierungsbeleg → Reservierungsbelege
• verb: liegt → liegen

Liegt is pronounced approximately like leegt in English spelling.

A rough guide:

• ie in German usually sounds like a long ee
• so liegt sounds close to leegt

The final g is not pronounced like a strong English g in everyday standard pronunciation; it often sounds closer to a soft k/t-like ending depending on accent and phonetics. For a learner, aiming for something close to leekt or leegt is usually understood, but the vowel should definitely be a long ee sound.

Normally, no. In this sentence, der sounds natural because you are talking about a specific reservation document.

So:

• Der Reservierungsbeleg liegt hier. = natural

Without the article:

• Reservierungsbeleg liegt hier = not normal standard German for this context

German usually uses an article with singular countable nouns unless there is a special reason not to.