Na konci jsme tleskali.

Because the preposition na here means at/on, and in the expression na konci it is followed by the locative case.

• konec = end
• na konci = at the end

This is a very common fixed expression in Czech.
Compare:

• na začátku = at the beginning
• na konci = at the end

So konci is the locative singular form of konec.

It means at the end or in the end part of something, depending on context.

In this sentence, the most natural meaning is:

• At the end, we applauded.

It usually refers to the end of an event, performance, speech, film, concert, etc.

Jsme is the present-tense form of být (to be) used as an auxiliary verb to form the past tense in Czech.

For we, the auxiliary is jsme:

• já jsem
• ty jsi
• on/ona/ono usually no auxiliary is written separately in the same way
• my jsme
• vy jste
• oni/ony/ona usually no separate auxiliary like in 1st/2nd person

So:

• jsme tleskali = we applauded / we were clapping

Tleskali is the past participle form used with my (we).

The infinitive is:

• tleskat = to clap, applaud

Past-tense forms agree with gender/number in Czech. For we, the form depends on who we refers to:

• tleskali = masculine animate or mixed group
• tleskaly = all-feminine group
• tleskala would be singular feminine, so not possible for we
• tleskalo would be singular neuter, also not possible for we

In many teaching examples, tleskali is often used as the default plural past form unless the speaker wants to make it specifically feminine.

It can mean either, depending on context.

Because tleskat is an imperfective verb, the past tense can express:

• an ongoing action in the past: we were clapping
• a general past action: we applauded

In this sentence, English would most naturally say we applauded. But grammatically, Czech tleskali does not force exactly the same distinction that English sometimes does.

Because Czech often omits subject pronouns when the verb already shows the person clearly.

Here, jsme already tells you the subject is we, so my is unnecessary.

• Na konci jsme tleskali. = natural
• Na konci my jsme tleskali. = possible, but more emphatic, like We were the ones applauding at the end

Czech usually leaves pronouns out unless there is contrast or emphasis.

Yes. Czech word order is flexible, and the sentence can be rearranged for emphasis or style.

Common possibilities:

• Na konci jsme tleskali. = neutral, natural
• Tleskali jsme na konci. = we applauded at the end
• Jsme tleskali na konci. = possible, but less neutral in ordinary speech

The original sentence sounds very natural because it starts with the time/location phrase na konci and then gives the action.

Usually yes. Tleskat means to clap or to applaud.

Depending on context, English may translate it as:

• to clap
• to applaud

For example:

• Děti tleskaly. = The children were clapping.
• Diváci tleskali hercům. = The audience applauded the actors.

So in your sentence, tleskali most likely means applauding at the end of something.

A rough pronunciation guide for an English speaker is:

• Na = nah
• konci = roughly KON-tsee
• jsme = roughly yz-meh or smeh in fast speech, depending on pronunciation habits
• tleskali = roughly TLES-kah-li

A few helpful points:

• c in Czech is always like ts
• j is like English y
• e is usually a short eh
• stress is normally on the first syllable of each word: NA KONci jsme TLESkali

Yes, and it would mean something slightly different.

• tleskali from tleskat = imperfective, focuses on the action as a process or general event
• zatleskali from zatleskat = perfective, focuses on a single completed act of applause

So:

• Na konci jsme tleskali. = At the end, we applauded / were clapping.
• Na konci jsme zatleskali. = At the end, we gave a clap / we applauded once as a completed action.

In many real contexts, both can work, but the aspect changes the nuance.

Yes. The past participle would normally change to agree with an all-female group:

• Na konci jsme tleskaly.

So:

• jsme tleskali = we applauded, where we includes at least one male or is a mixed group
• jsme tleskaly = we applauded, and the group is all female

This is a very important feature of Czech past tense.

It can mean either, depending on context.

For example:

• Seděl na konci stolu. = He sat at the end of the table.
• Na konci filmu jsme plakali. = At the end of the film, we cried.
• Na konci jsme tleskali. = At the end, we applauded.

So na konci is a general expression meaning at the end, and the surrounding context tells you what kind of end it is.

Because tleskat does not need one. It can stand on its own:

• Tleskali jsme. = We applauded.

If you want to say whom or what someone applauded, Czech often uses the dative:

• Tleskali hercům. = They applauded the actors.
• Tleskali mu. = They applauded him.

But if the sentence is just about the act of applauding, no object is necessary.