Learn French: C'était trop risqué, je n'aurais pas dû investir. - It was too risky, I should not have invested.

This is the conditionnel passé (past conditional) of the verb devoir (to have to / must). In the present conditional, je devrais means "I should". To put it in the past ("I should have") to express a regret, you use the conditional form of the helper verb avoir (j'aurais) plus the past participle of devoir (dû).

Where exactly does the negation ne ... pas go in the conditionnel passé?

Just like in the passé composé, the negation goes around the conjugated helping verb. Here, the helping verb is aurais, so the negative words wrap around it to make je n'aurais pas dû.

Why is investir in the infinitive when the English translation says "invested"?

In French, when you have a conjugated form of devoir, the main action verb that follows always stays in the infinitive. So even though the helping verb is in a past tense, you keep the action as investir (to invest).

Why does the past participle dû have a circumflex accent (^)?

The accent on dû is only there to tell it apart from the word du (meaning "some" or the combination of de + le). Note that if the participle needs to be feminine or plural, the accent disappears (for example, due or dus).