I am trying to make a the mustache in the picture above but can’t make the same thing. So far I have tried modeling the mustache but there is no hair and it’s just a flat mesh.
You can use hair particles.
Add a particle system and set it to hair. Choose a higher number for segments (e.g. 10).
Go to Particle Edit mode. Select some tips and scale them towards their center to create a pointy end segment. ⎈ CtrlNumpad+ select additional segments of the same strands and comb, smooth or cut them.
Unwrap the emitter object and use Noise Textures to create color variations in the material.
Use child particles, if the hair is not dense enough.
I would go with hair cards (= polygons with a few hairs mapped to them and a lot of transparency), you can find information about that here: http://wiki.polycount.com/wiki/HairTechnique This here shows the general (program independent) workflow, for the haird on top of the head, but you should be able to adapt it: tutorial from Athey Moravetz @ deviantart
You could also use the inbuilt hair system, depending on your hardware specs: https://docs.blender.org/manual/ja/dev/physics/particles/hair/index.html