После прогулки я вытряхнул песок из ботинок и вытер грязь с брюк.

Because the preposition после always requires the genitive case.

• Dictionary form: прогулка
• Genitive singular: прогулки

So после прогулки means after a walk / after the walk.

Russian often does drop subject pronouns when the verb ending makes the subject clear. But in the past tense, Russian verbs show gender and number, not person.

So вытряхнул could mean:

• I shook out if the context makes that clear
• he shook out in another context

Because of that, я is often included to make the subject explicit. If the context were already very clear, it could be omitted.

These are past tense, singular, masculine forms.

That tells you the speaker is male.

Compare:

• я вытряхнул, вытер = I did it, male speaker
• я вытряхнула, вытерла = I did it, female speaker
• мы вытряхнули, вытерли = we did it

So the verb form agrees with the speaker's gender in the past tense.

Because the sentence describes completed actions with a clear result:

• the sand was shaken out
• the dirt was wiped off

That is exactly the kind of situation where Russian normally uses the perfective aspect.

If you used imperfective forms such as вытряхивал or вытирал, it would sound more like:

• an ongoing process
• repeated/habitual action
• background description rather than a completed event

In both verbs, вы- suggests removal or bringing something out/off, often with a sense of completion.

• вытряхнуть = to shake out
• вытереть / past вытер = to wipe off / wipe away / wipe clean

So the prefix helps show that something was removed from somewhere.

They are the direct objects of the verbs, so they are in the accusative case.

In this sentence, their accusative forms happen to look the same as the basic form:

• песок → accusative песок
• грязь → accusative грязь

This is normal for many inanimate nouns in Russian.

Because the two prepositions describe different kinds of location:

• из = out of, from the inside
• с = off, from the surface

So:

• вытряхнул песок из ботинок = the sand was inside the boots
• вытер грязь с брюк = the dirt was on the trousers

This is a very natural Russian distinction.

Because after из, Russian uses the genitive case.

The basic plural is:

• ботинки = boots

But after из you need the genitive plural:

• из ботинок = out of the boots

So ботинок here is the genitive plural form.

Because брюки is a plural-only noun. It has no singular form in normal usage, like English pants or trousers.

After с, you need the genitive plural, and the genitive plural of брюки is:

• брюк

So:

• с брюк = off the trousers

Russian often leaves out possessive words like мой, мои when the ownership is obvious from context.

Here, if someone says:

• я вытряхнул песок из ботинок
• вытер грязь с брюк

it is naturally understood as my boots and my trousers, unless the context says otherwise.

English usually wants the possessive; Russian often does not.

Russian has no articles like a or the.

So после прогулки can mean:

• after a walk
• after the walk
• sometimes even something close to after walking

The exact English choice depends on context, not on a separate word in Russian.

Yes. Russian word order is flexible.

This sentence begins with После прогулки to set the scene first: After the walk...

You could also say:

• Я после прогулки вытряхнул песок из ботинок и вытер грязь с брюк.

That would still be correct. The difference is mostly one of emphasis and information flow, not basic meaning.

Russian often expresses this idea as:

• verb of removal
• plus a prepositional phrase showing where something was removed from

So:

• вытер грязь с брюк

literally works like wiped dirt off the trousers

This is a very common Russian pattern:

• снять пыль с полки = remove dust from the shelf
• стереть надпись с доски = erase the writing from the board
• смыть краску с рук = wash paint off the hands

So the structure in your sentence is very typical.