La consegna è stata ritardata dalla pioggia intensa di ieri.

This sentence is in the passive voice, which shifts the focus from the “doer” (the rain) to the “receiver” (the delivery). In the active you’d say:

• La pioggia intensa di ieri ha ritardato la consegna.
  But by using the passive, you emphasize the delivery itself:
• La consegna è stata ritardata …

Italian passive = appropriate tense of essere + past participle of the main verb.
1) essere in the same tense as the active auxiliary
2) past participle agrees in gender & number with the subject of the passive.
Here consegna is feminine singular, so:

• è (3rd-sing. present of essere)
• stata (fem.-sing. past participle of essere)
• ritardata (fem.-sing. past participle of ritardare)

In Italian prepositions like da combine (“elide”) with definite articles:

• da + il → dal
• da + la → dalla
• da + lo → dallo
• da + l’ → dall’
  Hence dalla pioggia = da
  • la pioggia.

di + a time expression indicates “of …” as in “belonging to or occurring in that time.”

• la pioggia di ieri = “yesterday’s rain.”
  You could also say ieri la pioggia intensa ha ritardato…, but di ieri directly attributes the rain to the previous day.

In Italian, descriptive adjectives typically follow the noun they modify:

• pioggia intensa rather than intensa pioggia (though both are grammatically possible, the post-noun position is more neutral/factual).
  Placing an adjective before the noun can add emphasis or a stylistic nuance.

It’s the passato prossimo in passive voice:

• è = present of essere
• stata = past participle of essere (to form the compound)
• ritardata = past participle of ritardare, agreeing with consegna.