What brushes to use:
I use synthetic sable brushes in various sizes of flat, round and filbert. And sometimes I'll use rubber stamps that I have designed. This is especially handy if I'm painting wallpaper in a scene.
Alkyd is so versatile that you could probably adopt and use any technique your imagination can come up with. You can do washes and glazing by diluting it with Liquin, an alkyd medium made by Winsor & Newton. Sometimes I even mix alkyd with gloss varnish to create a thin paint into which I dip a ruling pen for painting tree limbs or for drawing in lines around doorways and in hardwood floors. Most of the time, though, I paint in layers. I put down crude colors to start with and get the space filled in and then I add on and refine until I get what I want.
Mediums/additives you can use:
I haven't used many additives other than Liquin. Once or twice I've added a little extra linseed oil or stand coat to retard the drying. I used some cobalt drier once to speed up the drying time, but that was a big mistake. It made the painting so dull I had to repaint it.
I consider alkyd to be the most forgiving paint there is. It dries overnight, so if you don't like something, you simply paint over it.
You can mix alkyd with oil paint fully or partially. As well, you can use alkyd underneath oil colors but not the other way around because alkyd dries faster. I also wouldn't alternate paint layers with other fast-drying media like acrylics because of the different flexibilities in paint film.
Finishing it up:
My finished painting is dry within a couple of days (but can take a month to cure), and that's when I apply my varnish, a 50-50 mixture of MSA (mineral spirits soluble acrylic) varnish and Winsor & Newton's Conserv-art Gloss Varnish. This mixture gives me the right amount of body in my varnish, and a finish that's neither super-shiny nor really dull. I use three coats, sanding lightly between each with 600-grit sandpaper.
Paint like these masters:
Sharon Ellis, David Reed and Squeak Carnwath all work in alkyd.