How do you politely ask for things in Mandarin? I like to say please sometimes when I want to be polite to someone when asking them for something.  Is this customary in Mandarin?  

For example, if I wanted to ask for some water, I might ask my friend Li, in English, "would you please pour me some water?" In Mandarin, I only know to say wo xiang he shui, xie xie.  Also, I'm aware that saying thank you to a Chinese person can sometimes create a feeling of distance, and sometimes that is undesirable. 

So, Chinese people, and speakers, how do you politely ask for things, and how do you receive a statement such as "wo xiang he shui, xie xie"?  Does it come off as rude in any way?

PS - sorry I don't have chinese input on this device, but I think fluent speakers will know what I mean.
Politeness in Mandarin is expressed by using different politeness elements, which include politeness characters, wording or manner of speaking. Usualy one element is enough in one sentence, because using 2+ elements in the same sentence may sound too polite, causing a feeling of distance.

Would you please pour me some water? 请给我倒些水好吗？

Note: it is different from 我想喝水. Because 我想喝水 is not a request. If you tell me you want to drink some water, I will think, ok, no problem, go ahead and get some water for yourself, as you didn't ask me to get some water for you.
When making a request in Chinese, usualy we don't say 谢谢. Instead, we say 谢谢 when the request is either accepted or fulfilled.

A:您能帮我给他带个口信嘛？ B:可以。A:谢谢。---Request accepted but not fulfilled yet.
A:请给我倒杯水好嘛？ B:给你。A:多谢。---Request fulfilled。

Here are some examples of making polity requests in Mandarin:

您能帮我个忙嘛？ ---Politeness character 您 is an equivalent personal pronoun of 你 in Chinese showing your repect for others, including the elder, your superiors, and so on.
请帮我个忙。---Politeness character 请 is used here to show politeness when asking for a favor
我看，也只有你能帮我这个忙了。 ---Wording, which makes a request indirectly.
帮帮忙吧。 ---Manner of speaking, in a supplicatory way.
可怜可怜我们母子俩吧。---Wording + manner of speaking， which instigates pity.

By the way, the following are the expressions to use when someone says 谢谢/多谢 to you:

别客气 / 甭客气 / 不用客气 / 客气啥 / 太客气了 / 没事儿 / 见外啦 and a lot more.