Learn Hardcore Korean: bang yeyageul miri haeya haeyo. - You have to make a room reservation in advance.

방 (room)
예약을 (reservation + object marker)
미리 (in advance)
해야 해요 (must do / have to do)
Altogether: “You have to reserve a room in advance.” It follows the typical Korean S–O–V order (Subject omitted) + adverb + necessity expression.

Why is 을 attached to 예약?

을 is the object particle marking 예약 as what you are doing. Without it, the verb 하다 wouldn’t know what you’re “doing.” So 예약을 하다 = “to make a reservation.”

What role does 미리 play, and can I move it around?

미리 means “in advance” or “ahead of time.” It’s an adverb modifying 해야 해요. You can generally place it before or after the object:

미리 방 예약을 해야 해요.
방 예약을 미리 해야 해요.
Both are correct; the emphasis shifts slightly depending on placement but the meaning stays the same.

What is 해야 해요, and how does it express necessity?

해야 해요 comes from the verb 하다 (“to do”) plus the structure -아/어야 하다, which means “must” or “have to.” Conjugated politely in present tense, 해야 해요 = “you must do.” So 예약을 해야 해요 = “you have to make a reservation.”

Can I use 해야 돼요 instead of 해야 해요?

Yes. 해야 돼요 is another colloquial way to say “have to,” using 되다 instead of 하다.

예약을 미리 해야 해요.
예약을 미리 해야 돼요.
Both are perfectly natural; 돼요 can sound slightly more casual.

Why is there no subject in the sentence?

Korean often drops subjects when they’re obvious. Here, it’s a general statement: “(You) have to reserve a room in advance.” If needed for clarity, you could add:

여러분은 방 예약을 미리 해야 해요. (“As for you all, …”)
저는 방 예약을 미리 해야 해요. (“I have to …”)

How would I say this more casually to a friend?

Drop the polite ending -요 and use softer verb endings:

방 예약을 미리 해야 해.
Or even shorter: 미리 방 예약해야 해.
Both are fine among close friends.