Just how exactly do you pray at a shrine?

I've been looking up guides for praying at Shinto shrines in Japan and while they get the basics right, they all seem to differ regarding the finer details.

For example some guides say you should ring the bell before the monetary offering, but some say you should do it afterwards. Some guides say your hands must be straight when praying but others mention the right hand should be lower than the left.
While all the guides recommended using a 5-yen coin, some mention that any old coin will do while others say to avoid so-and-so coin as it may be bad luck.
At least a few of the guides mentioned bowing after the temizuya ritual and finally one of the guides mentioned providing your name and address during your pray, something not even the guides from the official tourism organization mentioned.

Is there any truly 100% correct way for praying at a shrine? I don't wanna make a laughing stock in front of locals but the inconsistencies between guides just makes me very worried!

There is no 100% correct way. There are millions of personal, shrine-specific and regional variations. But you can't go wrong with:
1) bow
2) bell (if available)
3) money
4) 2 bow
5) 2 claps
6) pray
7) bow

As Uji says, there is no 100% strict way - you are way over thinking things.
Shines (and temples) are a great way of getting rid of 1 and 5 yen coins, but many people offer with 100's and even 500 yen coins.
I have seen the offset-hand option when praying, and it is a nice touch, but a tiny detail.
Also, some major sites include simple guides on the order/number for the ritual (Meiji shrine for example).
No one will make fun of you if you do things slightly differently.

It is also nice to know that lots of Japanese people are confused about how to pray. It is not even rare to hear people clap at temples...

It is not even rare to hear people clap at temples...

Well, I don't know about other people, but clapping hands at buddist temples would be one thing that would make people's heads turn here in Japan.

And back to the question, yes, details differ depending on the shrine. A lot of times, the procedure is written on a board at the spot (often in Japanese language, but also often with illustrations).