Po rozcvičce začne lekce sestavou.

Po here means after, and when it is used in that time meaning, it normally takes the locative case.

The base form is rozcvička.
Its locative singular is rozcvičce.

So:

• rozcvička = warm-up
• po rozcvičce = after the warm-up

This is a very common pattern:

• po hodině = after the lesson
• po práci = after work
• po večeři = after dinner

For feminine nouns like rozcvička, the ending often changes from -a to -e / -ce in the locative.

Začne is from the verb začít, which is perfective.

In Czech, perfective verbs do not normally have a true present-tense meaning. Their present forms usually refer to the future.

So:

• začne = will begin / will start
• not is beginning in the usual sense

By contrast:

• začíná comes from začínat, the imperfective partner
• začíná means is beginning / begins in a general or ongoing sense

So in this sentence, začne fits because it describes a single completed starting point in the future sequence of events:

• first the warm-up
• then the lesson will start

The subject is lekce.

So the structure is:

• Po rozcvičce = after the warm-up
• začne = will begin
• lekce = the lesson
• sestavou = with a routine / by means of a routine / starting with a routine

A learner might expect lekce to be an object because it comes after the verb, but in Czech the subject does not have to come before the verb.

Here, lekce is in the nominative, so it is the subject.

Sestavou is the instrumental singular of sestava.

The instrumental is often used in Czech to express:

• the means by which something happens
• the way something is done
• what something begins/ends/is filled with

Here, začít něčím means to begin with something.

So:

• začne sestavou = it will begin with a routine

This is a very natural Czech structure. Compare:

• Přednáška začne diskusí. = The lecture will begin with a discussion.
• Večeře začala polévkou. = Dinner began with soup.

So sestavou is instrumental because it answers with what?

No. Nothing is missing.

In Czech, the idea of begin with something can be expressed directly by using the instrumental case, without a preposition.

So:

• začne sestavou is complete and grammatical

English needs with, but Czech does not here.

That is why a literal word-for-word translation can be misleading. Czech often uses case endings where English uses prepositions.

Yes. Czech word order is flexible, although not random.

This sentence could also appear as:

• Lekce začne po rozcvičce sestavou.
• Po rozcvičce lekce začne sestavou.

The basic meaning stays the same, but the emphasis changes slightly.

The given version,

• Po rozcvičce začne lekce sestavou.

sounds natural if after the warm-up is the starting point of the message.

Czech often places known or connecting information earlier, and newer or more important information later.

Because Czech has no articles like English a/an/the.

So:

• lekce can mean lesson, a lesson, or the lesson
• rozcvička can mean warm-up, a warm-up, or the warm-up
• sestava can mean routine, a routine, or the routine

The exact meaning depends on context.

In this sentence, English may naturally use the because the situation is specific, but Czech does not need to mark that.

Sestava literally means something like a set, sequence, routine, or combination of elements.

In exercise, dance, gymnastics, or teaching contexts, it often means a planned series of movements/exercises.

So here it likely means something like:

• a routine
• a sequence of exercises
• a set combination

It is not just any random movement. It usually suggests something structured.

Yes, in many contexts you could.

There is a difference in nuance:

• rozcvička = the warm-up as an activity/session
• rozcvičení = warming up, the process/result of warming up

So:

• Po rozcvičce = after the warm-up
• Po rozcvičení = after warming up

Both can be natural, but po rozcvičce sounds very idiomatic when talking about the warm-up as a scheduled part of a class or training session.

Because of the verb form and the cases.

Začne is 3rd person singular, and lekce is in the nominative, so lekce is the thing doing the action grammatically:

• lekce začne = the lesson will begin

If you wanted someone will begin the lesson, you would need a subject for the person and lekci in the accusative:

• Učitel začne lekci. = The teacher will begin the lesson.

So the case ending helps tell you who is doing what.

Yes, it is grammatical and understandable.

It sounds like something from a description of a class plan, exercise session, or lesson structure. For example, a teacher or coach might describe what happens in sequence:

• first the warm-up
• then the lesson begins with a routine

A slightly more explicit version might also be possible in context, but the original sentence is perfectly normal Czech.