Tropecé con el último escalón al bajar las escaleras.

Because the verb is tropezar and it has a spelling change in the yo form of the preterite:

• tropezar → tropecé

This happens because Spanish changes z to c before e to keep the same sound.

Similar examples:

• empezar → empecé
• almorzar → almorcé
• cruzar → crucé

So tropecé means I tripped.

Spanish often leaves out subject pronouns when the verb ending already makes the subject clear.

• tropecé = I tripped

The ending -é tells you it is yo in the preterite.
You could say Yo tropecé, but it is usually unnecessary unless you want emphasis or contrast.

Tropezar con means to trip over or sometimes to bump into depending on context.

In this sentence:

• Tropecé con el último escalón = I tripped over the last step

Spanish uses con after tropezar for the thing you trip over or run into.

Examples:

• Tropecé con una piedra. = I tripped over a stone.
• Me tropecé con Ana en la calle. = I ran into Ana in the street.

So you should learn tropezar con as a set expression.

Because escalón and escaleras are not the same thing.

• escalón = a step
• escalera = a staircase, flight of stairs, or sometimes ladder depending on context
• las escaleras often means the stairs

So:

• el último escalón = the last step
• las escaleras = the stairs

In English, step and stairs are also different, and Spanish makes the same distinction.

Al + infinitive is a very common structure in Spanish. It often means:

• when doing
• upon doing
• while doing

So:

• al bajar las escaleras = when going down the stairs / while going down the stairs

It comes from:

• a + el = al

More examples:

• Al entrar, saludó a todos. = When he came in, he greeted everyone.
• Al salir de casa, empezó a llover. = When I left the house, it started to rain.

Bajar can be used transitively in Spanish, especially with things like las escaleras, la calle, la montaña, etc.

So Spanish often says:

• bajar las escaleras = to go down the stairs

This is very natural in Spanish.

If you say bajar de las escaleras, it usually suggests coming down from the stairs rather than simply going down the stairs. That is a slightly different idea.

So in this sentence, bajar las escaleras is the normal choice.

Because in Spanish, las escaleras commonly refers to a staircase or the stairs as a whole, even though English may sometimes think of it as one unit.

That is why you often hear:

• Subir las escaleras = to go up the stairs
• Bajar las escaleras = to go down the stairs

Even if it refers to one staircase, Spanish often uses the plural form escaleras.

In Spanish, ordinal adjectives like primer, segundo, último, etc. commonly go before the noun.

So:

• el último escalón = the last step

That is the normal and natural order.

You may sometimes see adjectives after nouns in Spanish, but with último in this kind of meaning, putting it before the noun is standard.

The preterite is used because this is a completed action at a specific moment in the past.

• tropecé = I tripped
• It happened once and is finished.

If you used the imperfect, tropezaba, it would sound more like:

• I was tripping
• I used to trip
• I kept tripping

That does not fit this sentence as well, because tripping over the last step is a single completed event.

Yes, many speakers say me tropecé con..., and it is very common.

So you may hear:

• Tropecé con el último escalón
• Me tropecé con el último escalón

Both are used. The version without me is perfectly fine here. The reflexive form can sound slightly more common in everyday speech in some contexts, but both are understandable and natural.

Usually, yes. In this context, el último escalón normally means the last step in the staircase you were going down, often understood as the final one near the bottom.

However, the exact physical perspective depends on context. The sentence itself just says the last step. Since the person is bajando las escaleras, most people will picture the final step as they reach the bottom.

Yes, absolutely.

You can say:

• Tropecé con el último escalón al bajar las escaleras.
• Al bajar las escaleras, tropecé con el último escalón.

Both are natural. The second version puts more focus on the circumstance when going down the stairs.

A broad Spain pronunciation would be approximately:

• tro-pe-THÉ con el OOL-ti-mo es-ca-LÓN al ba-HAR las es-ca-YE-ras

A few notes:

• In most of Spain, z is pronounced like th in think, so tropecé sounds like tro-pe-THÉ.
• The stress falls on:
  • tropecé
  • último
  • escalón
  • bajar
  • escaleras

If you pronounce it with Latin American s instead of Spain th, people will still understand you perfectly.