Můj pes leží pod stolem.

Because můj has to agree with pes.

In Czech, possessive words like můj (my) change form depending on the gender, number, and case of the noun they go with.

• pes = masculine singular
• subject of the sentence = nominative case

So the correct form is:

• můj pes = my dog

Other forms would be used with different nouns, for example:

• moje kočka = my cat
• moje auto = my car

So moje pes is incorrect because moje does not match the noun pes here.

Pes is the subject of the sentence, so it is in the nominative case.

The dog is the thing doing the action:

• Můj pes = the dog
• leží = is lying

So pes stays in its basic dictionary form here.

A learner might also notice that pes is a masculine animate noun. That matters in some other cases, but in this sentence the important point is simply that it is the subject, so nominative is used.

Leží is the 3rd person singular present tense form of ležet.

So:

• ležet = to lie, to be lying
• leží = he/she/it is lying

Here it matches pes (dog), which is singular:

• Můj pes leží = my dog is lying

This verb is used for being in a lying position, not just for being somewhere in general.

Compare:

• Pes leží = the dog is lying
• Pes sedí = the dog is sitting
• Pes stojí = the dog is standing

So Czech often chooses a more specific verb than English does.

Because pod can take different cases depending on the meaning.

With pod:

• accusative = movement to under something
• instrumental = location under something

In this sentence, the dog is already there. It is a location, not movement.

So:

• Můj pes leží pod stolem. = My dog is lying under the table.

But if the dog were moving to that place, you would use accusative:

• Pes běží pod stůl. = The dog runs under the table.

So the choice depends on whether the sentence expresses position or direction.

Because after pod in a location meaning, Czech uses the instrumental case, and stůl changes form in the instrumental singular.

So:

• nominative: stůl = table
• instrumental singular: stolem

That is why you get:

• pod stolem = under the table

This noun also has a stem change:

• stůl -> stol-

You can see that same stem in other forms too, such as:

• stolu
• stolem

So pod stolem is the normal correct form.

Yes.

Czech has no articles, so it does not have separate words for a and the like English does.

That means stolem by itself can mean:

• a table
• the table

The exact meaning depends on context.

So pod stolem can be understood as:

• under a table
• under the table

In many real situations, context makes it obvious which one is meant.

No, Czech word order is fairly flexible.

Můj pes leží pod stolem is a very normal, neutral word order. It sounds like a straightforward statement.

But Czech can move parts around for emphasis or style, for example:

• Pod stolem leží můj pes.
• Leží pod stolem můj pes.

These all mean roughly the same basic thing, but the focus changes.

For example:

• Můj pes leží pod stolem. = neutral
• Pod stolem leží můj pes. = emphasis on under the table

So the original sentence is probably the best version for a learner to use first.

Yes, grammatically you can.

• Pes leží pod stolem. = The dog / a dog is lying under the table.

But if you say můj pes, you clearly specify that it is my dog.

Czech often leaves out information that is obvious from context, but omitting můj does change the meaning. Without it, the sentence is less specific.

So:

• Můj pes leží pod stolem. = My dog is lying under the table.
• Pes leží pod stolem. = The dog / a dog is lying under the table.

A rough guide:

• můj ≈ mooy
• pes ≈ pess
• leží ≈ le-zhee
• pod ≈ pot at the end, because Czech final voiced consonants are often devoiced
• stolem ≈ sto-lem

A couple of useful pronunciation notes:

• ž sounds like the s in measure
• ů is pronounced like a long oo
• Czech stress is usually on the first syllable of the word:
  • MŮJ pes LEží pod STOlem

A careful rough pronunciation of the whole sentence would be:

• Můj pes leží pod stolem -> mooy pess le-zhee pot sto-lem

Because Czech and English build the present tense differently.

In English, you usually say:

• is lying

That uses:

• the verb to be
• plus the -ing form

In Czech, the present tense is often expressed with just one verb form:

• leží

So leží already means is lying.

You do not need a separate word for is here.

Yes, but it means something slightly different in feel.

• Můj pes leží pod stolem. = My dog is lying under the table.
• Můj pes je pod stolem. = My dog is under the table.

The sentence with je focuses only on location.
The sentence with leží tells you both the location and the position of the dog.

So if you want to describe the dog specifically as lying down, leží is the better choice.