Ich stelle die Leiter an die Wand.

Stelle is the 1st person singular form of the verb stellen in the present tense.

• ich stelle = I place / I put / I set
• du stellst = you place
• er/sie/es stellt = he/she/it places

So in Ich stelle die Leiter an die Wand, the subject is ich, so the verb has to be stelle.

Here, stellen means to put something somewhere in an upright position.

German often distinguishes between different kinds of putting:

• stellen = put something so it ends up standing upright
• legen = put something so it ends up lying down
• setzen = put someone/something into a sitting position

A ladder usually ends up upright, so stellen is the natural verb.

That is why German says:

• Ich stelle die Leiter an die Wand.

not normally:

• Ich lege die Leiter an die Wand. if you mean leaning it upright

It is accusative, because die Leiter is the direct object of stellen.

You are putting the ladder, so the ladder is the thing directly affected by the action.

The reason it still looks like die is that feminine singular articles are the same in nominative and accusative:

• nominative: die Leiter
• accusative: die Leiter

So the form does not change, even though the grammatical role does.

Because an is a two-way preposition.

With two-way prepositions, German uses:

• accusative for motion toward a place / change of position
• dative for location / no movement

Here, the ladder is being moved to the wall, so German uses accusative:

• an die Wand = to/against the wall

Compare:

• Ich stelle die Leiter an die Wand.
  I put the ladder against the wall.
  → movement, so accusative

• Die Leiter steht an der Wand.
  The ladder is standing against the wall.
  → location, so dative

This is one of the most important patterns in German grammar.

In this sentence, an expresses the idea of being placed at / on / against a vertical surface like a wall.

German does not always use a separate word exactly matching English against. In many cases, an is the normal choice.

So:

• an die Wand stellen = put against the wall / put up against the wall

English and German divide up these meanings differently. A learner often wants a one-to-one match, but prepositions usually do not work that way.

Yes, it is very natural German.

With objects like ladders, chairs, or boards, an die Wand stellen often means to place them so they are leaning against the wall.

It is not just a random combination; it is a very normal way to describe this action.

You may also hear:

• Die Leiter steht an der Wand. = The ladder is against the wall.
• Ich stelle den Besen an die Wand. = I put the broom against the wall.

Because an takes the accusative here.

The noun Wand is feminine, and the feminine accusative article is die, so:

• nominative: die Wand
• accusative: die Wand
• dative: der Wand

So in this sentence:

• die Leiter = accusative direct object of stellen
• an die Wand = prepositional phrase with accusative because of motion toward the wall

Even though both articles are die, they belong to different parts of the sentence.

This is standard German main-clause word order:

• Ich = subject
• stelle = finite verb
• die Leiter = object
• an die Wand = prepositional phrase

So the structure is:

Subject + verb + object + place/direction

The important rule is that in a normal German main clause, the finite verb is in second position.

That is why stelle comes right after Ich.

You could also change the emphasis:

• Die Leiter stelle ich an die Wand.
• An die Wand stelle ich die Leiter.

In both of those, the verb stelle still stays in second position.

Yes, and this is a very useful thing to notice.

German has two different words spelled Leiter:

• die Leiter = ladder
• der Leiter = leader / manager / director

In your sentence, it is clearly die Leiter, because the meaning is ladder.

So the article matters a lot here:

• die Leiter = ladder
• der Leiter = person in charge

These are different nouns with different genders and different meanings.

This is a very common question.

• stellen = to place something so that it stands
  → usually transitive, so it takes an object
• stehen = to stand
  → usually intransitive, no direct object

Compare:

• Ich stelle die Leiter an die Wand.
  I put the ladder against the wall.

• Die Leiter steht an der Wand.
  The ladder is standing against the wall.

So stellen describes the action of putting it there, while stehen describes the resulting position.

Sometimes gegen can be used in German, but in this context an die Wand is the more natural and standard choice.

Very roughly:

• an die Wand often suggests placing something so it is at/against the wall, often resting there
• gegen die Wand can sound more like toward/against the wall in a stronger, more physical sense

For a ladder leaning against a wall, an die Wand stellen is the normal expression.

So if you are learning the safest, most idiomatic version, use:

• Ich stelle die Leiter an die Wand.

German often uses a more general verb plus a prepositional phrase where English might use a more specific verb.

English might say:

• I lean the ladder against the wall.

German often expresses that as:

• Ich stelle die Leiter an die Wand.

The idea of leaning is understood from the object (die Leiter) and the phrase an die Wand.

If you want to be more explicit, German can also use verbs related to leaning in some contexts, but stellen ... an die Wand is the most natural basic way to say this.