I'm trying to create a new language, but I need some advice. How do you determine what a new letter sounds like? Is there a pattern, or do I just make it up?
There are many ways of approaching the art of language invention. Some folks devise phonologies (sound systems) first; some people prefer to fashion logographies (writing systems) first. Still others like to write out a snippet of a song or poem first and try to sort out what just happened...
Whichever way you prefer to go, the basic answer to your question, depending on your philosophy of language invention, will be either the conlanger's answer: you make it up -- or else the glossopoet's answer: you discover the relation from within the language itself.
For example, if you came up with this letter:
you could either look through your chart and say: ah! that'll do nicely as the letter for [v]. Then it's just a matter of filling in the blank.
Or alternatively, you could delve into the history and culture of the people who speak the language and consider the prehistory of their writing systems (if any) and consider any sound symbology that might exist, and someone from that speech community might enter your dreams one night and teach you what sound that letter makes.
There may perhaps be a pattern: that too is something the conlanger will create or the glossopoet will discover along the way! Or there may not be a pattern at all.