Learn Italian: Ho bisogno di un po' d'acqua.

In Italian, "to need" is expressed with the idiomatic phrase avere bisogno di, which literally translates to "to have need of". Since ho means "I have", ho bisogno di means "I have need of" or simply "I need".

Why is there an apostrophe at the end of po'?

Po' is a shortened version of the word poco, which means "little" or "a small amount". The apostrophe is there to show that the end of the word was dropped. Together, un po' means "a little bit".

Why are there two words for "of" (di and d') in this sentence?

They belong to two separate phrases! The first di completes the phrase avere bisogno di (to have need of). The second one belongs to un po' di (a little bit of). The second di drops its vowel and becomes d' because the next word, acqua, starts with a vowel.

Where is the word for "I" in this sentence?

It is dropped! In Italian, the subject pronoun io (I) is usually left out because the verb form ho already tells us exactly who is doing the action.