Nach dem Regen grabe ich mit der Schaufel weiter, weil die Erde dann weicher ist.

Because nach in the sense of after takes the dative case.

• der Regen = nominative
• dem Regen = dative

So:

• nach dem Regen = after the rain

This is very common:

• nach dem Essen = after the meal
• nach der Arbeit = after work

German main clauses follow the verb-second rule. The conjugated verb must be in the second position.

Here, Nach dem Regen is placed first for emphasis, so the verb comes next:

• Nach dem Regen | grabe | ich ...

If you start with the subject, that also works:

• Ich grabe nach dem Regen mit der Schaufel weiter ...

Both are correct. The original just emphasizes after the rain.

grabe is the 1st person singular present tense of graben = to dig.

So:

• ich grabe = I dig / I am digging
• du gräbst
• er/sie/es gräbt

A learner may notice that du and er/sie/es have an umlaut, but ich grabe does not. That is normal for this verb.

Because mit always takes the dative case.

• die Schaufel = nominative
• der Schaufel = dative

So:

• mit der Schaufel = with the shovel / with the spade

Also, Schaufel is a feminine noun, which is why the dative article is der.

Both are possible, but they mean slightly different things.

• mit der Schaufel = with the shovel
• mit einer Schaufel = with a shovel

The definite article can sound natural if the shovel is already understood from the situation. German often uses definite articles in places where English might be a bit more flexible.

Here weiter means on, further, or continue.

So:

• ich grabe weiter = I keep digging / I continue digging

In this sentence:

• grabe ich mit der Schaufel weiter

the word weiter shows that the action is continuing, not just happening once.

Because weil introduces a subordinate clause, and in standard German subordinate clauses are separated by a comma.

So the sentence is divided like this:

• Nach dem Regen grabe ich mit der Schaufel weiter,
• weil die Erde dann weicher ist.

This is standard German punctuation.

Because weil creates a subordinate clause, and in German subordinate clauses the conjugated verb usually goes to the end.

So:

• weil die Erde dann weicher ist

not:

• weil die Erde dann ist weicher

This is one of the most important word-order patterns in German.

dann means then or at that point.

It refers back to nach dem Regen and makes the logic explicit:

• after the rain → then the soil is softer

So dann connects the two ideas clearly.

Erde can mean:

• earth / soil / ground
• Earth as the planet

The context tells you which meaning is intended. Since this sentence is about digging and soft ground, die Erde clearly means soil / earth / ground here.

Also, Erde is a feminine noun, so the nominative singular is die Erde.

weicher is the comparative form of weich.

• weich = soft
• weicher = softer

The idea is that the soil is softer than before or softer than when it is dry.

So:

• die Erde ist weich = the soil is soft
• die Erde ist weicher = the soil is softer

Because after sein (ist), the adjective is used predicatively, not directly before the noun.

Compare:

• die weiche Erde = the soft soil

  • here the adjective is before the noun, so it takes an ending

• die Erde ist weich / weicher = the soil is soft / softer

  • here the adjective comes after ist, so it does not take a gender/case ending

So weicher is just the comparative form itself, not an adjective ending.

Yes. For example:

• Ich grabe nach dem Regen mit der Schaufel weiter, weil die Erde dann weicher ist.

This has the same basic meaning. The difference is mainly emphasis:

• Nach dem Regen ... puts the time expression first
• Ich ... puts the subject first

German word order is flexible in this way, as long as the verb-second rule in the main clause is respected.