I am redesigning a logo for a client. For that I am designing the typography myself (no premade fonts). As I have never done that before I wonder if there are guidelines on determining the width of each glyph. I am using minuscules only. I determined some letters already from the preexisting logo(seen in black below), but am struggling with the "s" at the moment. The problem being that in the logo i got the "s" is a bit wide for my taste, but i have no idea how to determine the right width. 
Also it seems to me that the stem of the preexisting "s" is way to narrow. My research on the internet did not bear fruit so far, so any tips from a more experienced type designer than I am is very much appreciated.
Answer
You are trying to make a lowercase roman, with italic specifications but straight.
Following your design, there are some things to fix, check if this help you.
W1 – Character width, the character with of curved strokes are usually a little thicker, for the sample image is equal to the g:
W3 – Horizontal curved stroke width, the g must be fixed:
W2 – Character stroke width, the g curved stroke must be fixed. The curved strokes are usually a little thicker than the straight ones. On the images they have all the same width.
Using W2, rotated 65ยบ from X as the center of the new character.
With this grid you can get an approximation:
At the bottom of this image, the same s but made with the n width, i guess looks better.
Have a look to similar fonts like Waratah from myfonts.com
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