Proper form for "I would like to..." I am in doubt about the meaning of "xiǎng" and "yào":

As per my research on the web, if I want to say "I would like to ... " I would write "Wǒ xiǎng yào...". However, if instead, I wanted to say "I would like to eat noodles." I would write "Wǒ xiǎng chī miàntiáo."

Why doesn't "yào" appear in the second sentence? I am a bit confused about this.
Of course, if you want to you can say '我想要一份面’ or even '请给我带来一份 ...‘
In 'I would like' 'would' is the imperfect subjunctive of 'will'. ‘I would like' is incomplete, because a subjunctive needs a condition 'if ...'. Out of a strange, twisted form of over-politeness, it became popular in English to say 'I would like' short for 'I would like, if it is not too much trouble, ....' or some other condition after 'if ...'.

Now, you are in a restaurant. The restaurant sells food to make money. It is definitely not too much trouble to bring you what you want to eat. That is their job and how they make their living.

Forget 'I would like', that is not Chinese. Try 'for me the ...' or  'I'm ordering ...' 

Precede what you say with '请‘ and you are super polite.

Try ‘给我来一份面’ 或者 ‘我点一份拉面’ neither would be considered impolite.