После дождя земля на грядке стала мягкой.

Because после always takes the genitive case.

• дождь = nominative singular, the dictionary form
• дождя = genitive singular

So:

• после дождя = after the rain

This is a very common pattern in Russian:

• после урока = after the lesson
• после работы = after work
• после обеда = after lunch

Because земля is the subject of the sentence — it is the thing that changed state.

The basic structure is:

• земля стала мягкой
  = the earth/soil became soft

Here:

• земля = subject, so nominative
• стала = verb
• мягкой = describes the new state of the subject

Стала means became, while была means was.

So the sentence is emphasizing a change of state:

• земля была мягкой = the soil was soft
• земля стала мягкой = the soil became soft

In this sentence, the rain caused the soil to change, so стала is the natural choice.

After the verb стать (to become), Russian usually uses the instrumental case for the noun or adjective describing the new role or state.

So:

• земля стала мягкой

not usually:

• земля стала мягкая

Why мягкой?

• мягкий = masculine dictionary form
• feminine nominative = мягкая
• feminine instrumental = мягкой

Since земля is feminine and стать normally requires instrumental here, we get мягкой.

In standard modern Russian, instrumental is the normal choice after стать, so стала мягкой is what learners should use.

You may occasionally see nominative in some special styles, older language, or fixed expressions, but for normal everyday Russian, treat this as the rule:

• стать + instrumental

Examples:

• он стал врачом = he became a doctor
• она стала известной = she became famous
• вода стала холодной = the water became cold

На грядке is in the prepositional case because it answers the question where?

• грядка = garden bed / vegetable bed
• на грядке = on the garden bed / in the garden bed

With на, Russian often uses:

• prepositional for location: where?
• accusative for direction: to where?

Compare:

• земля на грядке = the soil in the garden bed
• класть землю на грядку = to put soil onto the garden bed

Грядка usually means a garden bed, especially a raised or prepared strip of soil where vegetables, herbs, or flowers are grown.

So земля на грядке means the soil in that cultivated patch of ground, not just soil in a general area.

Yes, Russian word order is fairly flexible.

This version is natural because it starts with the time/background phrase:

• После дождя = after the rain

Then it gives the subject and location:

• земля на грядке

Then the result:

• стала мягкой

Other word orders are possible, for example:

• Земля на грядке после дождя стала мягкой.
• На грядке земля после дождя стала мягкой.

These all mean roughly the same thing, but the emphasis shifts slightly depending on what comes first.

Russian has no articles like a or the.

So земля can mean:

• earth
• soil
• the soil

The exact meaning depends on context. In this sentence, English naturally uses the soil or just soil, but Russian does not need a separate article word.

The adjective comes from мягкий (soft).

Its feminine forms are:

• nominative: мягкая
• genitive: мягкой
• dative: мягкой
• accusative: мягкую
• instrumental: мягкой
• prepositional: мягкой

Here it is instrumental feminine singular, because it agrees with земля and follows стала.

So:

• земля = feminine singular
• стала мягкой = became soft

In this sentence, soil is the best practical meaning.

Земля can mean several things depending on context:

• earth / the Earth
• land
• ground
• soil

Because the sentence mentions на грядке (in the garden bed), the meaning is clearly soil here.

The main stresses are:

• послЕ
• дождЯ
• землЯ
• на грЯдке
• сталА
• мЯгкой

A rough pronunciation guide:

• pas-LYE dazh-DYA zem-LYA na GRYAT-kye sta-LA MYAK-kay

A few useful notes:

• дождя has a soft дь sound before я
• грядке begins with a consonant cluster that may feel difficult at first
• мягкой has a soft мя and ends with something like -koy

Usually на грядке is the natural choice.

Russian normally says:

• на грядке = in/on the garden bed

Even though English often says in the garden bed, Russian prefers на with грядка.

So for learners, the best phrase to remember is:

• земля на грядке
• овощи на грядке = vegetables in the bed

Using в грядке would sound unusual or wrong in most normal contexts.