I have the kanji 寧 and it ON-YOMI is ネイ how do you read it NEI or NEE.

I've listened to several audios where the reading is NEI, but in compounds like 寧静 the reading is NEE-SEI.

The problem is i don't know how to learn it, should i learn it like NEI for 寧 and keep in mind that in compounds the reading will be changed to NEE?

Anyone can point me to a webpage where i can learn the reading rules of double vowels for kanji?

Generally speaking,

えい ＝ ええ
おう ＝ おお
いう ＝ ゆう

everything else should be pronounced according to the rules.

Well i know that rule but:
丁寧 is red as TEE-NEE
寧日 is red as NEI-JITSU with an actual I instead of an prolonged E.

All this is according to the audio found on http://www.edrdg.org/

If 寧日 reading is a rule exception there is no issue since i can learn it as an exception, if there is a rule where the reading changes depending on the following kanji id like to learn the rule instead of just memorizing compounds.

Just follow the above rules and you'll be fine.

If you want to get technical, according to the NHK pronunciation dictionary it's /neːd͡ʑit͡sɯᵝ/ ,　it's a long え

えい! is pronounced ei.
思う is pronounced omou - the えい and おう rules don't apply when crossing morpheme boundaries.

Someone better than me please explain 永遠.

Well, this might not be helpful, but, depending on the region of Japan, it could be either "nee" or "nei"

The "nee" pronunciation has become dominant because it's the "Standard Japanese" (ie, a specific dialect of Tokyo, spoken by a specific group of people) pronunciation. I hate having to teach my students that it's pronounced "sen see" or "ee go", and I know of at least one native speaker teacher who disliked it too. However, all the native speaker lecturers at my uni are from the general Tokyo region, and since it's correct for them, that's how we have to do it.

[Zgarbas]

I think that teaching standard language is the norm in any language. It's better to choose your dialect or give it a personal note after you've mastered the language. Especially as a foreigner, people assume that your using non-standard pronunciation is a mistake rather than a choice; you never win (even in English, I've had people correct my pronunciation of privacy as /prɪvəsi/ at times, same for cicada as /sɪˈkɑ də/). I sometimes hear other foreigners use regional words or slang and I also tend to assume that they're doing it due to a misunderstanding. At least Standard Japanese is actually standardised, unlike other languages (*glares at English*), which makes it easier.

Zgarbas-san no iutoori. I tend to play with Japanese the way I play with English. I know it isn't a good idea (especially when my Japanese is so poor) but in speech my exuberance tends to run away with me. I think I may have been built as a cheer-up doll originally.

But I am aware that there is a high likelihood of people thinking I am just getting things wrong, and I do in fact hold back a lot of little jokes and twists knowing that they are likely to be seen as ignorance.

I think if one actually lives in an area and starts using its standard pronunciation (or "dialect" as it is condescendingly called) that is a different matter. Otherwise the standard language is, for better or worse, the standard language. And after all, in an age of mass communication having a standard language is not a bad idea!

I see, so there isn't any grammatical rule that changes the reading (like if the kanji is at the end of the word it's pronounced SEI and if it's at the beginning of the word it's pronounced SEE) it's just a dialect issue.

Then of course I'll go with the standard reading and learn it that way. But is good to know so i can keep in mind that some people will use SEI instead of SEE and it's the same word with a somewhat muddied pronunciation.

Thank You for the explanation and pointers!