Learn Italian: Dobbiamo ottimizzare il lavoro di oggi.

You simply attach it directly to the front to make riottimizzare. When adding the iterative prefix ri- (which means to do an action again) to a verb that starts with a vowel, you usually just stick them together.

Could we attach ri- to the modal verb instead, saying ridobbiamo ottimizzare?

No, the prefix must attach to the specific action that is being repeated. Since we need to repeat the optimizing rather than the obligation itself, the prefix goes on the infinitive, giving us Dobbiamo riottimizzare.

What base word does ottimizzare come from?

It derives from the adjective ottimo, which means excellent or optimal. By adding the suffix -izzare, which works exactly like the English suffix -ize, it becomes a verb meaning to make something optimal.

Why is today's work translated using di, as in il lavoro di oggi?

English treats time words almost like people, allowing them to possess things with an apostrophe-S. Italian does not do this with adverbs of time. You have to phrase it literally as the work of today, linking the noun and the time with the preposition di.