The stir plate method was the first yeast starter technique I used in my brewery. It is probably that way for many, since it was widely considered the "one true way" to ensure you had enough healthy yeast for the job ahead.
What you need:
Stirplate - no need for a mega-powerful unit here, you just need to keep it moving.
Flat bottomed glass vessel - Erlyenmeyer Flasks are popular for this and have that mad scientist lab vibe. A 2 or 3 liter size is plenty for most brewers. Go for borosilicate glass if you can.
Stir bar - magnetic and the key piece that makes the whole thing work. Most stir plates include at least one, but good to have a spare.
Foam stopperor aluminum foil - no airlocks here, you need the starter to breathe in that good O2 for health and growth.
Starter Wort - You can make it as needed or buy pre-packaged.
You've collected your equipment, sanitized and clean, and yeast. Let's get this starter started.
Make Your Starter Wort - shoot for an OG of 1.036 - 1.040. 100 grams of dry malt extract to 1 liter of water will get you there. Boil for 10 minutes to sterilize it, then cool. Alternatively, you can grab a can of Propper Starter and save this step if you're pressed for time, or like the convenience.
Pour into your sanitized flask
Add yeast and cover/insert sanitized foam stopper
Start the stir plate - here's where I see a lot of brewers go wrong. You don't need a whirling vortex of wort and yeast, just a gentle motion that causes a slight indentation in the middle and keeps everything moving. Get too overzealous here and you can actually cause excess stress to the yeast and create some undesirable flavors.
Time your starter to pitch at high krausen - ok, this is my anecdotal opinion but I get faster starts and more complete attenuation when I pitch at high krausen vs. chilling and decanting the starter. Aim for 18-24 hours from yeast pitch, and pitch the whole thing.
Done correctly your starter will produce a sufficient amount of viable yeast to get the job done. Don't get hung up on counts and calculators. Start with a quality yeast that has been handled well, follow these guidelines, and you'll consistently produce reliable and thorough fermentations. Better fermentations equal better beer, and isn't that what we're after? Starters aren't hard and no one should be intimidated by them.