Mit einer Heftklammer befestige ich den Merkzettel an der Rechnung.

German often puts something other than the subject in the first position for emphasis or style. Here, Mit einer Heftklammer is placed first to highlight how the note is attached.

Even though that phrase comes first, the conjugated verb still has to stay in second position in a main clause:

• Mit einer Heftklammer befestige ich den Merkzettel ...
• first position = Mit einer Heftklammer
• second position = befestige

So the subject ich comes after the verb. This is completely normal in German word order.

Because mit always takes the dative case.

The noun die Heftklammer is feminine, so in the dative singular:

• nominative: eine Heftklammer
• dative: einer Heftklammer

That is why the sentence has:

• mit einer Heftklammer = with a staple / paper clip

Heftklammer usually means staple. In some contexts, learners may confuse it with a paper clip, but the most common meaning is staple or something used for stapling papers together.

So:

• mit einer Heftklammer befestigen = to attach with a staple

If the speaker meant a paper clip more clearly, German might use Büroklammer.

Because den Merkzettel is the direct object of befestigen.

The verb befestigen means to fasten / attach / secure, and the thing being attached is the direct object. Merkzettel is masculine:

• nominative: der Merkzettel
• accusative: den Merkzettel

So:

• Ich befestige den Merkzettel ...
• I attach the note ...

This is about the two-way preposition an.

With two-way prepositions, German uses:

• accusative for direction/movement toward a destination
• dative for location/position

Here, the note ends up attached on/at the bill, so German treats it as the resulting position:

• an der Rechnung = on / attached to the bill

This is very common with verbs like befestigen, where the focus is often on where something is fixed.

A learner may expect motion and therefore accusative, but German often uses dative after verbs of fastening because the thing is being secured in a position.

Merkzettel means a note, memo, or reminder slip.

It comes from:

• merken = to notice / remember
• Zettel = slip of paper, note

So a Merkzettel is a small written note meant to remind someone of something.

Befestigen means to attach, fasten, or secure.

It is a normal and useful verb, especially in written or neutral German. It can be used for physically attaching things:

• ein Schild befestigen = attach a sign
• ein Bild an der Wand befestigen = fasten a picture to the wall

Depending on context, everyday German might also use other verbs such as:

• anheften = attach, staple on
• anklammern = clip to
• festmachen = fasten, secure

But befestigen is a good general-purpose verb.

German expresses that idea through the preposition an plus case, rather than using a separate word exactly like English to.

So:

• an der Rechnung literally means something like at/on the bill
• in natural English, this often becomes to the bill or onto the bill, depending on context

Languages do not always divide meanings in the same way. German uses an here where English prefers to in the phrase attach something to something.

Yes, absolutely. That is probably the most neutral word order for many learners:

• Ich befestige den Merkzettel mit einer Heftklammer an der Rechnung.

This version starts with the subject ich, which is often easier to understand.

The original version:

• Mit einer Heftklammer befestige ich den Merkzettel an der Rechnung.

puts more emphasis on the method: with a staple.

Both are correct.

Here is the full breakdown:

• Mit einer Heftklammer

  • mit takes dative
  • einer Heftklammer = feminine singular dative

• ich

  • subject, so nominative

• den Merkzettel

  • direct object, so accusative
  • masculine singular accusative

• an der Rechnung

  • an here takes dative
  • der Rechnung = feminine singular dative

So the structure is:

• dative prepositional phrase
  • verb
    • subject
      • accusative object
        • dative prepositional phrase