Asking someone to do something

Hi, this is something that has been confusing me for some time. I was wondering how to ask something politely in japanese. A lot of japanese guides say to use the form "てください", however it feels like I'm giving a command rather than asking something. While digging deeper in my japanese studies I also found the "てくれませんか" or "ていただけませんか" forms.
So I was wondering, for example if I want to ask someone, say a stranger, to speak slowly in a polite way, what form would I use?
ゆっくり話してください。
ゆっくり話してくれませんか？
ゆっくり話していただけませんか？
And is "てください" normally used to ask for someone to do something ?

That is the difference (in English, let’s say) among:
- Please speak slowly.
- Can you/won’t you speak slowly for me please?
- Wouldn’t you speak slowly for me please?

While all are defined as expressions of “making a request,” the first one not being a question but a statement, it could sound somewhat blunt. So the 2nd and the 3rd ones would be more roundabout and thus more polite.

So if you can say either the 2nd or 3rd one, I guess either of them would be more polite, particularly if you are talking to strangers, thus better.

ゆっくり話してくれませんか？ is probably an abbreviated (or mixed ) form of ゆっくり話してくださいませんか？
くださる is a polite form of くれる.
give me a slow speaking. may (can, could, would) you give me a slow speaking ?

ゆっくり話していただけませんか？ is a polite form of ゆっくり話してもらえますか？
いただく is a polite form of もらう.
may (can, could, would) I receive a slow speaking ?

we use those expressions depending on the situations such as the places, the counterpart, etc.

1.
You are correct in that 〜てください is a command, not a request. It's a polite command, since 〜てください means "please [do]," but it's still a command. So saying 「ゆっくり話してください。」 would be the same as saying "Please speak slowly," which is something I probably wouldn't say to a stranger in Japanese or English.

「ゆっくり話してくれませんか？」 and 「ゆっくり話していただけませんか？」 are both OK for making the request of a stranger, but personally I'd go with 「ゆっくり話していただけませんか？」.

いただけませんか comes from いただきます, which is itself a polite way of saying "receive" or "have someone do something for you." So comparatively, 「ゆっくり話していただけませんか？」 carries a bit more of a feeling that the other person speaking more slowly would be a special kindness to you that you'd appreciate, not something they should do for you as a matter of course.

2.
「And is "てください" normally used to ask for someone to do something ?」

〜てください matches up pretty closely to saying "Please [do]" in English. So while it's a polite phrase, it's not really asking someone to do something so much as telling them to do it. Because of that, it's mainly used in situations where there's an expectation that the other person can and should comply.

Personally, I rarely use 〜てください when I want someone to do something, and don't think I've ever used it when speaking to a stranger. Instead, I pretty much always use 〜ていただけませんか or 〜てもらえますか. That's also my way of communicating in English, though. I'm much more likely to say "Could you 〜 for me?" or "Can I have you 〜 for me?" instead of just "Please 〜."

I see, as I thought it's not the most polite but it's weird how many guides say to use "てください". Thank you very much for your detailed answers, I understand the usage of these expressions better now.

Glad to be of help!

「it's weird how many guides say to use "てください"」

The vocabulary/phrases section of travel guidebooks (as opposed to dedicated language-learning textbooks) are probably fond of 〜てください for a couple of reasons.

1.
Travel guidebooks are generally written with the image that you'll be in Japan as a tourist, and so most of your interactions will be with people working in the service sector (waiters, taxi drivers, hotel clerks, etc.). In those cases, there generally is an expectation that the person you're talking to will comply with what you want done ("Please drive me to Tokyo Tower," "Please give me a wakeup call at 8 AM," etc.). That said, I'm still more likely to use 〜ていただけませんか or 〜てもれえますか even when dealing with service sector workers, but that's my personality.

2.
〜てください is shorter and easier to remember than 〜ていただけませんか. ください is also sort of a two-for-one vocabulary word since it's perfectly fine to use a noun followed by ください when someone asks you what you want. For example, if a waitress asks you what you'd like to drink, and you say おちゃください ("Tea please") that's a natural-sounding way to respond.

Grammatically, おちゃいただけませんか would also be OK, but since the waitress is already offering to bring you a drink, and tea is a very common drink in Japan, the extra politeness of おちゃいただけませんか might seem a little overly dramatic, so おちゃください would probably be the more natural-sounding choice.

I see, it's easier to learn for a tourist then. Thank you very much for the extra info !

I think guides suggest "てください" because it's the easiest way to say something politely.

Even though it's a command in a grammatical sense, it's still courteous. If I were a beginner in Japanese language, I wouldn't want to jump into an expression as long as "ていただけませんか". I wouldn't be able to remember it correctly.

Meanwhile, a not-polite command would be things like "しなさい" or "して" or "しろ".