An deiner Stelle würde ich die Bluse heute nicht bügeln, sondern erst morgen auf einen Kleiderbügel hängen.

It is an idiomatic way to say if I were you or in your position.

Literally, an deiner Stelle means something like in your place / at your position, but in normal English the natural meaning is if I were you.

So:

An deiner Stelle würde ich ...
= If I were you, I would ...

Because Stelle is part of a fixed expression here, and it takes the dative:

an + dative → an deiner Stelle

Since Stelle is feminine, the possessive dein- becomes deiner in the dative singular.

So:

• nominative: deine Stelle
• dative: deiner Stelle

In this sentence, German uses the dative form.

German main clauses follow the verb-second rule: the finite verb must be in the second position.

Here, An deiner Stelle comes first, so the finite verb würde must come next:

An deiner Stelle | würde | ich ...

If the sentence started with ich, then it would be:

Ich würde an deiner Stelle ...

Both are grammatically fine, but the original sentence puts emphasis first on An deiner Stelle.

This is Konjunktiv II, often used for:

• hypothetical situations
• polite suggestions
• advice

So würde ich ... bügeln means I would iron ...

In this sentence, it gives advice in a softer, less direct way:

An deiner Stelle würde ich ...
= If I were you, I would ...

It is not past tense. It is a conditional/hypothetical form.

Yes. It is closely related to the fuller idea:

Wenn ich an deiner Stelle wäre, würde ich ...

That means:

If I were in your position, I would ...

In everyday German, An deiner Stelle würde ich ... is a very common shorter way to say the same thing.

Because würde is the finite verb, and the main action verb goes to the end as an infinitive.

So:

• würde ... bügeln
• würde ... hängen

In the second part of the sentence, würde ich is not repeated, but it is understood:

..., sondern erst morgen auf einen Kleiderbügel hängen.

This is basically short for:

..., sondern ich würde sie erst morgen auf einen Kleiderbügel hängen.

So the second infinitive hängen also stays at the end.

Because the first idea is negated:

nicht bügeln

When German says not this, but that instead, it usually uses:

nicht X, sondern Y

So here the meaning is:

• not iron it today
• but rather hang it up tomorrow

aber can mean but, but sondern is specifically used when the second part replaces or corrects a negated first idea.

Compare:

• nicht heute, sondern morgen
• nicht bügeln, sondern hängen

Here erst means not until or only.

So erst morgen means:

• not until tomorrow
• only tomorrow

It emphasizes that tomorrow is the earliest suitable time, not today.

This is a very common use of erst in German.

Die Bluse is the direct object of bügeln, so it is in the accusative.

Because Bluse is feminine, the accusative singular article is still die, so it looks the same as the nominative:

• nominative: die Bluse
• accusative: die Bluse

It is also understood as the object of hängen in the second part, even though it is not repeated.

So the sentence means:

I would not iron the blouse today, but rather hang the blouse up tomorrow.

German just avoids repeating die Bluse.

Because this sentence describes movement toward a destination: putting the blouse onto a hanger.

With two-way prepositions like auf, German uses:

• accusative for direction/destination (where to?)
• dative for location (where?)

So:

• auf einen Kleiderbügel hängen = to hang it onto a hanger
• auf einem Kleiderbügel hängen = to be hanging on a hanger

Here the blouse is being moved onto the hanger, so German uses the accusative:

auf einen Kleiderbügel

Here it means to hang something up — an action you do to an object.

So in this sentence:

die Bluse ... auf einen Kleiderbügel hängen
= to hang the blouse on/onto a hanger

Compare:

• Ich hänge die Bluse auf einen Kleiderbügel.
  = I hang the blouse onto a hanger.

• Die Bluse hängt auf einem Kleiderbügel.
  = The blouse is hanging on a hanger.

So the same verb form appears, but the grammar tells you whether it means an action or a state.

Because it is understood from the first part.

The full version would be something like:

An deiner Stelle würde ich die Bluse heute nicht bügeln, sondern sie erst morgen auf einen Kleiderbügel hängen.

But German often omits repeated words when the meaning is clear. That makes the sentence sound more natural and less repetitive.

So the object die Bluse is shared by both verbs:

• die Bluse nicht bügeln
• (die Bluse) auf einen Kleiderbügel hängen