Nach dem Waschen bügele ich die Bluse mit dem Bügeleisen, bevor ich sie auf den Kleiderbügel hänge.

Because nach takes the dative case here.

• das Waschen = the washing
• after nach, it becomes dem Waschen

So:

• das Waschen → nominative
• dem Waschen → dative

This is the same kind of change you see with other neuter nouns:

• nach dem Essen = after the meal / after eating
• nach dem Training = after training

In this sentence, nach dem Waschen means after washing.

Because it is being used as a noun, not as a verb.

Normally, waschen means to wash and is written with a lowercase letter. But in nach dem Waschen, the action is turned into a noun, often called a nominalized infinitive. In German, all nouns are capitalized, so it becomes Waschen.

Compare:

• Ich wasche die Bluse. = I wash the blouse.
• Nach dem Waschen... = After washing...

So the capital letter shows that Waschen is functioning like a noun.

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

Here, the sentence starts with the time expression Nach dem Waschen. That whole phrase takes the first position, so the verb has to come next:

• Nach dem Waschen | bügele | ich die Bluse ...

Even though English would usually say After washing, I iron..., German still keeps the verb in second position.

If you started with the subject instead, you would get:

• Ich bügele die Bluse nach dem Waschen...

That is also grammatically possible, though it changes the emphasis a bit.

Because bevor introduces a subordinate clause, and in German subordinate clauses, the conjugated verb normally goes to the end.

So:

• bevor = before
• bevor ich sie auf den Kleiderbügel hänge = before I hang it on the hanger

The normal subordinate-clause pattern is:

• conjunction + subject + other elements + verb

So here:

• bevor
  • ich
    • sie auf den Kleiderbügel
      • hänge

This is one of the most important word-order patterns in German.

Because the second part is a new clause, and German clauses need their own subject unless the subject is otherwise clearly omitted in a special structure.

In English, we also say:

• Before I hang it up

not just

• Before hang it up

So German does the same:

• bevor ich sie ... hänge

Even though the subject is the same person as in the main clause, it still has to be stated again.

Sie refers to die Bluse.

Since Bluse is a feminine noun, the matching pronoun is sie.

In this sentence:

• die Bluse = the blouse
• ich bügele die Bluse
• bevor ich sie ... hänge = before I hang it

So English uses it, but German uses sie because pronouns agree with the grammatical gender of the noun, not with biological sex.

Because mit always takes the dative case.

The noun is das Bügeleisen:

• nominative: das Bügeleisen
• dative: dem Bügeleisen

So:

• mit dem Bügeleisen = with the iron

This phrase tells you the instrument used to do the action.

A useful rule:

• mit = almost always with, and it always requires dative

Because auf is a two-way preposition. That means it can take either:

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

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

• auf den Kleiderbügel hänge = hang onto the hanger

If you were describing where it already is, you would use the dative:

• Die Bluse hängt auf dem Kleiderbügel. = The blouse is hanging on the hanger.

So the contrast is:

• motion/change of position → auf den Kleiderbügel
• location → auf dem Kleiderbügel

Because Kleiderbügel is masculine: der Kleiderbügel.

With the two-way preposition auf plus movement, you need the accusative. The masculine accusative article is den.

So:

• nominative: der Kleiderbügel
• accusative: den Kleiderbügel

That is why the sentence says:

• auf den Kleiderbügel

They do similar time-related jobs, but they work differently.

1. nach

Nach is a preposition, so it is followed by a noun phrase:

• nach dem Waschen = after washing

2. bevor

Bevor is a subordinating conjunction, so it introduces a whole clause with a conjugated verb:

• bevor ich sie auf den Kleiderbügel hänge = before I hang it on the hanger

So:

• nach
  • noun
• bevor
  • clause

A related comparison:

• nach dem Waschen = after washing
• nachdem ich die Bluse gewaschen habe = after I have washed the blouse

Both can express time, but the grammar is different.

Mostly, this is something you have to learn together with the noun. German grammatical gender is often not predictable from meaning alone.

Here:

• das Bügeleisen = the iron
• der Kleiderbügel = the clothes hanger
• die Bluse = the blouse

There are sometimes patterns, but they are not completely reliable. For learners, the safest method is to memorize nouns with their articles:

• die Bluse
• das Bügeleisen
• der Kleiderbügel

That will help you form correct pronouns and cases later.

Yes. German uses compound nouns very frequently.

Bügeleisen

This is made from:

• bügeln = to iron
• Eisen = iron

So das Bügeleisen literally means something like ironing iron.

Kleiderbügel

This is made from:

• Kleider = clothes
• Bügel = hanger / frame / bow, depending on context

So der Kleiderbügel means clothes hanger.

Understanding compounds can make German vocabulary much easier to decode.

Because German often uses the present tense to describe:

• routines
• general habits
• actions in a sequence

So this sentence sounds like a normal description of what someone does:

• Nach dem Waschen bügele ich die Bluse...
• ...bevor ich sie auf den Kleiderbügel hänge.

English often does the same:

• After washing, I iron the blouse before I hang it on the hanger.

So the present tense here is completely natural.

Yes. That would also be correct.

With a noun phrase:

• Nach dem Waschen bügele ich die Bluse...

With a full clause:

• Nachdem ich die Bluse gewaschen habe, bügele ich die Bluse...

The version with nach dem Waschen is more compact and elegant here. The version with nachdem is more explicit because it includes the full action and subject.

So both are possible, but the original sentence sounds smoother and less repetitive.