I use oil-primed pre-stretched belgian linen canvas for my oil paintings, and either Fabriano Tiziano or Hahnemuhle Bugra paper for my soft pastels (depending on size).
Regardless of medium, I begin by enlarging my source materials, drawing a grid over them, and transferring the "bones" of the picture onto a matching grid on my pastel paper or canvas. I have experimented with using other methods, such as a projector, or a fellow artist's recommendation of a type of rub transfer using paint instead of charcoal, but I come back to the grid as the safest and best method, if somewhat tedious. For pastels, I use pencil; for oil paintings, I use crayon. I then apply a workable fixative or shellac.
Painting Techniques in Oils and in Soft Pastels.


OILS
To prepare for an oil portrait, I spend a few days setting up my palette. Skin tones include a wide range of colors, and I mix a spectrum of several shades from light to dark. I use a silicone icecube tray as a container and organizer: the icecube tray can then be saran-wrapped and stored in the freezer over night to help the paint last longer, as I am a very detailed, thorough, take-my-time sort of an artist, and I will work on a painting for months.
I use Mona Lisa paint thinner for diluting and cleaning while painting, and Winsor & Newton non-toxic brush cleaner for safe and thorough brush care at the end of each day.
I paint my underpainting in raw sienna or sometimes raw umber. I get as detailed as I possibly can, recreating every light, shadow, curve and line in monotone. For areas of the background that I plan to complete more quickly, I may apply an extremely thin layer of alkyd medium to "couch" the canvas, saturating it and making it receive the paint more easily.
And then I simply paint what I see, from dark to light, from skin to features to hair to clothing, etc. I layer light over dark, paint in wide planes and then scumble the transitions. Often, on a face, there are a lot of transitions.
When I complete an oil portrait, I oil out any matte patches and apply a gloss varnish over the whole.
PASTELS
Pastel paintings require little preparation, other than mounting the paper to board. I have an ENORMOUS collection of soft pastels, accumulated over a lifetime, containing every color in the rainbow and probably every different brand as well. Unisom brand has the deepest blacks and whitest whites, but is very soft, almost too soft for me, so I use it sparingly when deep/opaque colors are needed.
I like to use a green or blue-green sheet of paper for portraits, because the blood coursing through our skin adds a blue/green undertone, and the colored paper serves as a sort of built-in underpainting.
As with oils, I work from dark to light. My kneaded eraser helps ensure I stay on track. I use my pinky finger prolifically to mix colors on the page, create the appearance of smoothness (pastels are naturally rough on the textured paper), and blend transitions. Sometimes my poor little pinky aches at the end of the day!
When a pastel is completed, I spray it lavishly with LaSceaux Protective Fixative, and prefer it framed under museum glass, with an apron built into the bottom of the matting to prevent any build up of particle dust.

Techniques are subject to change, as I am always learning and improving.