There are many ways to create lettering as vector art. This is one technique I use daily for both commercial and personal work.
Start with a preliminary sketch, scan the sketch and open the image file in Photoshop. Adjust to image size for use as a drawing template in Illustrator. I tend to work at a 40" width for most lettering projects. The resolution is very low 72 or 75 dpi as the file will not be used for print reproduction.
Adjust the levels as the objective is to posterize the image as a bitmap tiff for import to Illustrator.
Posterize the image.
Save the file as a tiff image.
Save the file as a bitmap image to reduce the files size.
Open the image file in Illustrator
Create a template layer with the image and adjust the value to 10%.
Create a new layer for use as the vector path drawing layer.
Begin drawing vector lines. Try to keep the paths as smooth as possible.
Continue drawing path placement and adjusting beizer handles and follow the template image.
Select the path and adjust the overall weight to match the hairline quality of the lines you desire. With the size of this particular lettering I changed the stroke weight to 6 points with round end caps and corners. Round caps and corners will soften the endpoints of the paths instead of finishing the paths with sharp pointy ends.
With the paths selected go to the Illustrator Object pull down menu, select sub menu Paths and then Outline Stroke. This will turn the path into an object which will be modified by adjusting the points along the path including the bezier handles.
Select points along the path, move and adjust to paths to follow the template image.
Continue adjusting paths of all the letters in your composition. This is not meant to be a fast process. Take your time as the goal is to produce beautiful smooth curves for each letter.
After you adjust the paths of each letter view your work in non preview mode. This will allow you to see what needs to be fine tuned as the lettering composition continues. The letterforms will change as the vector drawing process continues.
Some paths may not match up to the template image. I tend to turn off the template image after the basic letterforms are setup. I will move and adjust paths depending on how the letters relate to one another. The most important aspect of this process is to enjoy what you are creating regardless of the time it may take to adjust all the lines, shapes, curves and bezier handles.
I often use the Pathfinder filters to unite all the vector paths into one compound path. This technique allows for cleanup of any irregularities.
This image shows an odd transition between the letters o and m of a lettering piece created in 2013. To get a smooth flow all the paths were selected and the Compound Path Unite filter was applied.
All the paths transformed to one compound path and the irregular line segment was adjusted to a smooth flowing stroke between letters.
Points on a path are often deleted or moved while lettering in vector format. It's all part of the process.