Learn Hardcore Japanese: kaigi no zyunbi ha zikan ga kakarimasu.

It links two nouns, making a possessive/attributive relationship. 会議の準備 means “the preparation for the meeting” or “the meeting’s preparation.” This XのY pattern is the normal way to say “preparation for X” (e.g., 旅行の準備, “trip preparation”).

Why is は used after 準備?

は marks the topic: “As for the meeting preparation, ….” The sentence then comments on that topic with 時間がかかります (“time is required/taken”). The overall pattern is a classic topic–comment: Xは Yが V.

Could I use に instead of は (会議の準備に時間がかかります)? What’s the difference?

Yes. 会議の準備に時間がかかります means “It takes time for meeting preparation,” with に marking the thing for which time is required.
Nuance:

Xは時間がかかります = topical (“As for X, it takes time”), often contrastable.
Xに時間がかかります = neutral statement of where the time goes.
Xには時間がかかります = combines both roles (topic + target), often slightly contrastive/emphatic.

Why is 時間 marked with が and not を?

Because かかる is intransitive and treats the resource that is consumed (time/money) as the grammatical subject. The fixed phrase is 時間がかかる (“time is taken”). 時間をかかる is ungrammatical.

Can I say 会議の準備が時間がかかります?

No. That’s an unnatural “double が.” Use either:

会議の準備は時間がかかります (topic–comment), or
会議の準備に時間がかかります (marks what the time is spent on).

What exactly does かかります mean? What’s the dictionary form?

Dictionary form: かかる. Here it means “to take (time)” or “to cost (resources).” Other senses of かかる exist (e.g., “to hang”), but with 時間が it specifically means “to take time.”
Basic conjugations:

Plain non-past: かかる
Polite non-past: かかります
Plain past: かかった
Polite past: かかりました
Plain negative: かからない
Polite negative: かかりません
Te-form: かかって

What’s the difference between 時間がかかる and 時間をかける?

時間がかかる (intransitive): “It takes time” (time is consumed, not emphasizing intention).
Example: 会議の準備に時間がかかります。
時間をかける (transitive): “to spend time (intentionally) on ….”
Example: 会議の準備に時間をかけます。 (I/we make a point of spending time on it.)

How do I say how much time it takes?

Place the amount before かかる:

2時間かかります。 (It takes 2 hours.)
2時間くらい／ほどかかります。 (about 2 hours)
Emphasis: 2時間もかかります。 (as much as 2 hours) / 2時間しかかかりません。 (only 2 hours)

How do I put this in past, negative, or talk about the future?

Past: 会議の準備は時間がかかりました。 (It took time.)
Negative: 会議の準備は時間がかかりません。 (It doesn’t take time.)
Non-past in Japanese covers present, habitual, and future; context shows which:
明日の会議の準備は時間がかかります。 (The prep for tomorrow’s meeting will take time.)

Is 会議を準備する correct?

It’s not natural in everyday Japanese. Use 会議の準備をする (“do the meeting’s preparation”) or a verb like 会議を設定する/開く (“set up/hold a meeting”) depending on what you mean.

Where is the English “it” in this sentence? Who is the subject?

Japanese often omits “it.” Grammatically, 時間 is the subject (marked by が). So the sentence literally says, “As for meeting preparation, time is required.”

Can I omit parts of the sentence?

Yes, if context makes them clear:

（会議の）準備は時間がかかります。 (Drop 会議の if “meeting” is obvious.)
準備には時間がかかります。 (General “preparation” takes time.)
時間がかかります。 (It takes time—when the topic is understood.)

Should かかる be written with kanji?

You’ll often see it in kana: 時間がかかる. Writing 時間が掛かる is also acceptable, but modern style prefers kana for this verb because it has many meanings.

When would I use 時間はかかります instead of 時間がかかります?

Use 時間は to contrast or highlight the “time” part:
お金はかかりませんが、時間はかかります。 (It doesn’t cost money, but it does take time.)

How do you pronounce the whole sentence?

Kaigi no junbi wa jikan ga kakarimasu.
Kana: かいぎのじゅんびはじかんがかかります。
Natural chunking: [会議の準備は] [時間が] [かかります] (topic → subject → verb).