Learn Hardcore Korean: naeil sikdang yeyageul haesseoyo. - I made a restaurant reservation for tomorrow.

내일 means tomorrow. In Korean, time expressions usually go before the object and verb, so you’ll often see 내일 (or another time word) right at the start.

Is 식당 the direct object here, and what does it mean?

Yes. 식당 means restaurant, and it’s the thing being reserved. It functions as the direct object of the verb 예약을 하다.

Why do we say 예약을 했어요 instead of just 예약 했어요?

예약 is a noun (“reservation”), and when you treat it as the object of 하다 (“to do”), you attach the object particle 을. So grammatically complete form is 예약을 했어요, though in casual speech Koreans sometimes drop particles.

Can I simply say 식당 예약 했어요 in conversation?

Yes. Dropping 을 is very common in everyday, informal Korean. 식당 예약 했어요 is understood perfectly well, especially in spoken contexts.

What is 했어요 exactly, and what level of politeness does it convey?

했어요 is the past-tense, polite–informal ending of 하다. So 예약을 했어요 literally means did a reservation in a polite but not overly formal style.

How would you make this sentence more formal?

Switch to the formal polite ending -습니다:
내일 식당 예약했습니다.

Why don’t we see a subject like 저는 in the sentence?

Korean often omits the subject when it’s clear from context. Here it’s assumed you (or “I,” depending on the situation) made the reservation.

Is the word order the same as in English?

No. Korean follows Subject-Object-Verb order. Even though the subject is omitted here, you see time (내일) → object (식당 예약을) → verb (했어요), unlike English’s S-V-O.

Could I use the verb form 예약하다 directly, as in 예약했어요?

Yes. 예약하다 is the verb “to reserve.” Koreans often merge noun plus 하다 into one verb, so 예약했어요 (reservation-did-+past) is perfectly natural and interchangeable with 예약을 했어요.