הוא מטגן בצל במחבת, ואני שמה את המחבת על הכיריים.

Hebrew present-tense verbs agree with the subject’s gender and number.

• הוא מטגן = he is frying / he fries
• אני שמה = I am putting / I put said by a female speaker

So:

• מטגן is the masculine singular present form
• שמה is the feminine singular present form

With אני, the verb still changes for gender:

• אני שם = I put (said by a man)
• אני שמה = I put (said by a woman)

In Hebrew, the present tense usually does not use a separate word meaning am / is / are.

So:

• הוא מטגן בצל literally looks like he frying onion
• but it means he is frying onion or he fries onion

This is normal Hebrew structure.
In the present tense, Hebrew often just uses the subject + present participle form of the verb.

מטגן comes from the verb לטגן, meaning to fry.

In this sentence:

• הוא מטגן = he is frying

Related forms:

• לטגן = to fry
• מטגן = frying / fries (masculine singular present)
• מטגנת = frying / fries (feminine singular present)

So the form tells you both the action and the gender/number of the subject.

את is used before a definite direct object in Hebrew.

Compare:

• הוא מטגן בצל = he is frying onion / an onion / some onion
• הוא מטגן את הבצל = he is frying the onion

In your sentence, בצל is indefinite, so there is no את.

That is why later you do get:

• את המחבת = the pan

because המחבת is definite.

במחבת means in a pan or in the pan, depending on context.

It is made from:

• ב־ = in
• מחבת = pan / frying pan

Hebrew often attaches short prepositions directly to the noun:

• ב־ = in
• ל־ = to
• כ־ = like/as
• מ־ = from

So:

• במחבת = in a pan / in the pan

In this sentence, it is most naturally understood as in a pan.

This is the difference between indefinite and definite nouns.

• מחבת = a pan
• המחבת = the pan

So:

• במחבת = in a pan
• את המחבת = the pan

Hebrew uses ה־ as the definite article, like English the.

It is very common to first introduce something as indefinite and then refer back to it as definite:

• He is frying onion in a pan, and I put the pan on the stove.

That sounds natural in English too.

ו־ means and.

So:

• ואני = and I

Hebrew usually attaches ו־ directly to the following word instead of writing it separately.

Examples:

• הוא ואני = he and I
• ואני שמה = and I put / and I am putting

Good question. In this sentence, שמה is the verb form from לשים (to put), and it means:

• I put / I am putting (female speaker)

This form can confuse learners because Hebrew has other similar-looking words, but here the grammar makes it clear it is a verb:

• ואני שמה את המחבת = and I put the pan

If the speaker were male, it would be:

• ואני שם את המחבת

So here שמה is definitely the feminine present-tense form of לשים.

Because המחבת is a definite direct object.

Hebrew uses את before a direct object when that object is definite, for example with:

• ה־ (the)
• a proper name
• a possessive expression

So:

• אני שמה מחבת = I put a pan
• אני שמה את המחבת = I put the pan

Notice that את itself does not mean the.
It is just a marker showing that the following noun is a definite direct object.

Yes, הכיריים usually means the stove / the burners / the cooktop.

Grammatically, it is a plural form, even though in English we often translate it as a singular idea.

So:

• כיריים = stove / stovetop / burners
• הכיריים = the stove / the stovetop / the burners

This is one of those nouns where Hebrew and English do not match perfectly in number.

על means on.

So:

• על הכיריים = on the stove / on the burners

This is the natural preposition for placing a pan on top of a cooking surface.

Some common Hebrew prepositions are:

• ב־ = in
• על = on
• ל־ = to

That is why the sentence uses:

• במחבת = in a pan
• על הכיריים = on the stove

Yes. Hebrew present tense often covers both ideas.

So:

• הוא מטגן בצל can mean:
  • he fries onion
  • he is frying onion

And:

• אני שמה את המחבת על הכיריים can mean:
  • I put the pan on the stove
  • I am putting the pan on the stove

In actual translation, the surrounding context tells you which English version sounds more natural.

The sentence follows a very common Hebrew word order:

• הוא מטגן בצל במחבת
  • he
    • frying
      • onion
        • in a pan
• ואני שמה את המחבת על הכיריים
  • and I
    • putting
      • the pan
        • on the stove

So the basic pattern is often:

• subject + verb + object + other details

That is similar to English in many cases, which makes this sentence relatively beginner-friendly.