Auf meinem Schreibtisch liegen ein Locher und ein Tacker, aber die Büroklammern sind schon wieder weg.

Because auf is a two-way preposition. It can take:

• dative for a location: where something is
• accusative for a direction: where something is going

Here, the hole punch and stapler are already on the desk, so this is a location, and German uses the dative: auf meinem Schreibtisch.

Compare:

• Die Sachen liegen auf meinem Schreibtisch. = The things are on my desk.
• Ich lege die Sachen auf meinen Schreibtisch. = I put the things onto my desk.

Also, Schreibtisch is masculine: der Schreibtisch, so the dative form of mein is meinem.

That is normal German main-clause word order. German uses the V2 rule: the finite verb must be in the second position.

So if you put the location first:

• Auf meinem Schreibtisch = position 1
• liegen = position 2

Then the subject comes after that:

• ein Locher und ein Tacker

A more neutral version would be:

• Ein Locher und ein Tacker liegen auf meinem Schreibtisch.

Both are correct. The original sentence puts the location first for emphasis or scene-setting.

Because the subject is plural: ein Locher und ein Tacker = one hole punch and one stapler.

Two singular nouns joined by und make a plural subject, so the verb must also be plural:

• Ein Locher liegt ... = singular
• Ein Locher und ein Tacker liegen ... = plural

German often prefers a position verb where English might simply use to be.

Here, liegen means to lie / to be lying and is used for things that are resting somewhere, especially not in an upright position.

So:

• Ein Locher liegt auf dem Schreibtisch.
• Ein Tacker liegt auf dem Schreibtisch.

This sounds natural in German.

Using sein is not always impossible, but liegen is more idiomatic when talking about where an object is positioned. German commonly distinguishes:

• liegen = lie, be lying
• stehen = stand, be standing
• hängen = hang, be hanging

Because the first two nouns are singular, while Büroklammern is plural.

• der Locher → ein Locher
• der Tacker → ein Tacker
• die Büroklammer → plural die Büroklammern

So:

• ein is the nominative masculine singular indefinite article
• die here is the nominative plural definite article

Also, German has no plural form of the indefinite article. So you cannot say an equivalent of a paper clips. If you wanted indefinite plural, you would simply say:

• Büroklammern sind weg.

Here it is plural.

German die can mean:

• feminine singular: die Lampe
• plural: die Lampen

So you have to look at the noun and the verb:

• Büroklammern ends in -n, which shows plural
• the verb is sind, which is also plural

So die Büroklammern sind ... clearly means the paper clips are ...

Singular would be:

• Die Büroklammer ist weg.

Schon wieder is a very common expression meaning again already, but in natural English it is usually something like:

• yet again
• once again
• already again
• again, as usual

It often suggests annoyance, frustration, or disbelief.

So die Büroklammern sind schon wieder weg means not just that they are gone again, but that this keeps happening.

Weg means gone, away, or missing.

In this sentence, it describes a state:

• Die Büroklammern sind weg. = The paper clips are gone.

It does not mean they are physically walking away, of course. It just means they are no longer there.

This is a very common German pattern:

• Mein Schlüssel ist weg. = My key is gone.
• Das Geld ist weg. = The money is gone.

Because aber is a coordinating conjunction, like but in English.

It connects two main clauses, but it does not force the verb to the end, and it does not itself count as the first element of the clause in the same way a fronted phrase does.

So the second clause keeps normal main-clause word order:

• aber die Büroklammern sind schon wieder weg

That is different from a subordinating conjunction like weil, where the verb goes later:

• ..., weil die Büroklammern schon wieder weg sind.

From the sentence, the nouns are:

• der Schreibtisch = desk
• der Locher = hole punch
• der Tacker = stapler
• die Büroklammer = paper clip

You can see this in the article forms:

• meinem Schreibtisch shows that Schreibtisch is masculine dative singular
• ein Locher and ein Tacker show masculine nominative singular
• die Büroklammern is plural

You cannot always guess noun gender from meaning, so it is best to learn each noun with its article:

• der Schreibtisch
• der Locher
• der Tacker
• die Büroklammer

Because in German, all nouns are capitalized.

So in this sentence, these are capitalized because they are nouns:

• Schreibtisch
• Locher
• Tacker
• Büroklammern

This is standard German spelling and one of the easiest ways to spot nouns when reading.