Die Gläser trockne ich lieber mit einem Tuch ab, statt sie lange auf dem Tisch stehen zu lassen.

German often puts the element you want to emphasize first. Here, Die Gläser is the direct object, but it has been moved to the front for focus or contrast.

Even when something other than the subject comes first, German still keeps the conjugated verb in second position:

• Die Gläser | trockne | ich ...

So the subject is still ich, even though it comes after the verb.

A more neutral version would be:

• Ich trockne die Gläser lieber mit einem Tuch ab ...

Both are correct, but the original puts extra attention on the glasses.

Because the verb has to agree with the subject ich.

The full verb is abtrocknen. In the present tense:

• ich trockne ... ab
• du trocknest ... ab
• er/sie/es trocknet ... ab

So trockne is the correct 1st person singular form.

The verb is abtrocknen, which is a separable verb.

In a main clause, separable prefixes split off:

• Ich trockne die Gläser ab.

So in your sentence:

• Die Gläser trockne ich ... ab

The main part of the verb, trockne, appears in second position, and the prefix ab goes to the end of the clause.

Because mit always takes the dative case.

So:

• mit einem Tuch = with a cloth

Tuch is a neuter noun, so the indefinite article in the dative singular is einem.

Compare:

• der Löffel → mit einem Löffel
• die Gabel → mit einer Gabel
• das Tuch → mit einem Tuch

Because auf is a two-way preposition:

• dative for location: where?
• accusative for direction: where to?

Here the glasses are already on the table, so this is a location, not movement:

• auf dem Tisch stehen = to stand on the table

If there were movement toward the table, you would use accusative:

• Ich stelle die Gläser auf den Tisch.
  = I put the glasses onto the table.

Lieber means rather or preferably.

It is the comparative form of gern, which is often used to talk about liking to do something:

• Ich trockne die Gläser lieber mit einem Tuch ab.
  = I’d rather dry the glasses with a cloth.

So lieber shows preference between two options:

1. drying them with a cloth
2. leaving them on the table for a long time

Statt means instead of or rather than.

It introduces the alternative action:

• statt sie lange auf dem Tisch stehen zu lassen

So the sentence means:

• I prefer to dry the glasses with a cloth, instead of leaving them on the table for a long time.

You may also see anstatt, which means the same thing in many contexts.

Sie refers back to die Gläser.

It is in the accusative here because it belongs to lassen:

• etwas stehen lassen = to leave something standing

So:

• sie ... stehen zu lassen
  = to leave them standing

Even though die Gläser is plural, the pronoun is still sie in both nominative and accusative plural, so the form does not change.

Here, stehen lassen means to leave standing or more naturally to leave sitting there.

With objects like glasses, cups, plates, or bottles, German often uses stehen lassen when something is left in place instead of being cleared away or dealt with.

So:

• die Gläser auf dem Tisch stehen lassen
  = to leave the glasses on the table

It does not necessarily mean you are thinking about the physical posture of the glasses in English; it is just the normal German wording.

Because this is an infinitive construction after statt, and the zu attaches to lassen, not to stehen.

The basic verbal expression is:

• etwas stehen lassen = to leave something standing

When this whole expression goes into a zu-infinitive clause, German says:

• etwas stehen zu lassen

So the pattern is:

• verb + infinitive + zu lassen

This is normal German usage with lassen in this kind of structure.

It is accusative, because it is the direct object of abtrocknen.

The confusion comes from the fact that for plural nouns, die can be both nominative and accusative:

• nominative plural: die Gläser
• accusative plural: die Gläser

You can tell it is accusative because the actual subject is ich, shown by the verb form trockne.

Yes. A more straightforward version would be:

• Ich trockne die Gläser lieber mit einem Tuch ab, statt sie lange auf dem Tisch stehen zu lassen.

This is often easier for learners to process because the subject comes first. The original sentence is not unusual, though; it just uses fronting for emphasis.