Один тапок лежит под кроватью.

Because тапок is masculine singular, and один has to agree with it.

So here you get:

• один = masculine
• тапок = masculine noun
• both are in the nominative singular

Compare:

• один тапок = one slipper
• одна тапочка = one slipper, if you use the feminine noun тапочка
• одно окно = one window

Russian one changes form depending on gender, number, and case.

Because тапок is singular: one slipper.

• тапок = one slipper
• тапки = slippers / multiple slippers

A learner may expect тапки because slippers usually come in pairs, but Russian can absolutely talk about just one slipper: один тапок.

It is in the nominative case.

That is because один тапок is the subject of the sentence — it is the thing doing the “lying”:

• Один тапок = the subject
• лежит = lies / is lying
• под кроватью = under the bed

The nominative is the basic dictionary form for the subject of a sentence.

Лежит is the 3rd person singular present tense of лежать.

So:

• лежать = to lie
• лежит = lies / is lying

It is singular because the subject is singular: один тапок.

A useful point: Russian does not have a separate form like English is lying. The present tense лежит can cover both:

• lies
• is lying

The exact meaning depends on context.

In Russian, the choice between лежать, стоять, and висеть often depends on the object’s position.

• лежать = to be lying, be in a horizontal position
• стоять = to be standing, upright
• висеть = to be hanging

A slipper is thought of as a thing lying on the floor, so лежит is natural.

This is a very Russian way of describing location. English often just says is, but Russian often prefers a more specific verb.

Because под takes different cases depending on meaning.

For location (where something is), под usually takes the instrumental:

• под кроватью = under the bed

For movement toward a place, под takes the accusative:

• положить под кровать = to put under the bed

So here, since the slipper is already there and not moving, Russian uses the instrumental: под кроватью.

Кроватью is the instrumental singular of кровать.

• dictionary form: кровать = bed
• instrumental singular: кроватью

This noun is a feminine soft-sign noun, and many nouns of that type form the instrumental singular with -ью.

So:

• кровать → кроватью
• дверь → дверью
• тетрадь → тетрадью

Yes, it could.

• Тапок лежит под кроватью = A slipper is lying under the bed / The slipper is lying under the bed
• Один тапок лежит под кроватью = One slipper is lying under the bed

Adding один makes the idea of one explicit. It may sound like:

• there is exactly one slipper there
• maybe the other slipper is missing
• the speaker is contrasting one slipper with something else

So один adds a sense of number or emphasis, not just basic existence.

Mostly it means one, but in some contexts it can feel a little like English a single or one used for introduction.

However, Russian does not have articles like a and the. So:

• Тапок лежит под кроватью can mean A slipper is under the bed or The slipper is under the bed
• Один тапок лежит под кроватью more clearly means One slipper is under the bed

So один is not a true article. It still keeps its basic meaning of one.

No, Russian word order is fairly flexible.

Один тапок лежит под кроватью is a natural, neutral sentence. But you could also say:

• Под кроватью лежит один тапок.
• Тапок лежит под кроватью.

The meaning stays similar, but the focus changes:

• Один тапок лежит под кроватью → focuses early on one slipper
• Под кроватью лежит один тапок → starts with the location under the bed
• Тапок лежит под кроватью → simpler, less emphasis on the number

Russian word order often helps show what is new, important, or emphasized.

The usual stress is:

• оди́н
• та́пок
• лежи́т
• под
• крова́тью

So the whole sentence is pronounced:

Оди́н та́пок лежи́т под крова́тью.

Stress matters in Russian, because it is not always predictable and can affect pronunciation of the vowels around it.