Learn Hardcore Japanese: watasi ha tugi no kaigi de mizikaku hanasimasu. - I will speak briefly at the next meeting.

は marks the topic (what the sentence is about). Here, the topic is 私 (I/me).
が marks the grammatical subject and often adds focus/contrast. 私が would mean “It’s I (and not someone else) who will speak briefly,” which sounds contrastive.
In neutral statements about oneself, 私は is fine, and often 私 is omitted entirely.

Do I need to say 私 at all?

Often no. Japanese drops pronouns when clear from context. Very natural: 次の会議で短く話します.

What does の do in 次の会議?

It links the modifier 次 (next) to 会議 (meeting) to form a noun phrase: “the next meeting.” It’s the standard way to say “next NOUN.”

Why is it 会議で and not 会議に?

で marks the place/setting where an action happens: 会議で話す = speak at the meeting.
に marks time, destination, or target: 会議に参加する (attend a meeting), 会議に間に合う (be on time for the meeting).
会議に話す is unnatural in this sense.

What form is 短く, and why not 短い?

短い is an i-adjective (short).
To modify verbs (make an adverb), i-adjectives change い → く: 短く話す = speak briefly.
For na-adjectives, use に: 静かに話す (speak quietly), 簡潔に話す (speak concisely).

Does 短く mean “quickly”?

No. 短く = briefly (short in length). For speed, use:

早く話す = speak early/quickly (timing/speed).
速く話す = speak fast (speed).

How can the polite present 話します mean “will speak”?

Japanese has no dedicated future tense. The non-past (話します) covers present/future; the time phrase (次の会議で) supplies the future meaning. To be explicit:

Intention: 話すつもりです
Plan/schedule: 話す予定です
Officially decided: 話すことになっています

Is 話します transitive or intransitive here? Why no object?

Here it’s intransitive (“to speak”). If you want to specify the content:

計画について短く話します (talk briefly about the plan) is common/natural.
計画を短く話します also occurs but is less common/formal than について with 話す.

Can I say 話をします instead?

Yes. 話をする means “to have a talk,” slightly more casual in feel. In business, verbs like 説明する, ご説明する, 発表する are more specific and often preferred.

What’s a more natural way to say “briefly” in business Japanese?

手短に話します (I’ll keep it brief)
簡潔にご説明します (I’ll explain concisely)
要点だけお話しします (I’ll cover only the main points) All are very natural in meetings.

Can I reorder the words, like 私は短く次の会議で話します?

Japanese word order is flexible, but the neutral flow is: time/occasion/place → manner → verb.

Best: 次の会議で短く話します
短く次の会議で話します sounds a bit odd.

How polite is 話します? Do I need honorific/humble forms?

話します is polite (-ます) but not honorific/humble.
When addressing clients/superiors about your own action, use humble: お話しします / ご説明いたします.
Very polite example: 次回の会議で手短にご説明いたします.

Pronunciation tips?

は as a topic particle is pronounced “wa.”
Readings: 私=わたし, 次=つぎ, 会議=かいぎ, で=で, 短く=みじかく, 話します=はなします.
Note ぎ is a hard “g,” and し is “shi.”

Is 次の the same as 来週の or 次回の?

次の会議: the next meeting in the sequence.
次回の会議: more formal/explicit “the next session/meeting.”
来週の会議: the meeting next week (not necessarily the very next one).

Why are there spaces between the words? Japanese doesn’t usually use them, right?

Correct—normal Japanese doesn’t use spaces. Standard writing: 私は次の会議で短く話します. The spaces are just for teaching segmentation.

If I want to say “I’ll keep it short,” can I say 短くします?

You need an object: 説明を短くします (I’ll make the explanation short). Without an object, use 手短にします or 手短に話します.

What’s the difference between 話す, 言う, and しゃべる here?

話す: to speak/talk (general, appropriate).
言う: to say (a specific utterance); 言います here would be odd.
しゃべる: to chat/chatter (casual); avoid in formal meetings.

Could I say 発表します instead of 話します?

Yes, if you mean “present” (give a presentation). Then you might say:

次の会議で短く発表します
次回の会議で簡潔に発表します Use 説明します if you’re explaining, 発表します if you’re formally presenting.