You absolutely can purchase a starter over the interwebs, or, if you're lucky, acquire one from a family member or friend. But you don't actually need to: All you need is flour and water and, of course, yeast and bacteria, which are literally EVERYWHERE. There are a lot of different ways to do this, but this method has worked consistently in our test kitchen and builds a robust and flavorful starter.
scale with tare function; quart-sized, wide-mouthed glass jars with lids
To begin: Mix together 125 grams flour and 125 grams water with a clean hand in a medium glass bowl. Cover the bowl with a tea towel and let sit undisturbed at room temperature until the mixture is full of bubbles and has nearly doubled in size, usually 2 to 3 days. During this time, yeasts and bacteria from the air and from the flour and probably from you will set up housekeeping in the bowl (see Cook's Note).
For daily feeding: Peel back any crust that may have formed and transfer 20% of the culture (50 grams) to a clean, wide-mouthed jar. Stir in 100 grams flour and 100 grams water, loosely screw on the lid and stash at room temperature for 24 hours. (The culture will have a stinky-sour smell at this point.) Discard the rest of the original mixture.
Repeat step 2 every 24 hours for 5 days. By then the culture should smell yeasty-sweet-sour, which means you're ready to put the starter to work.
If your culture isn't showing signs of life after 3 days, go ahead and start feeding. If, after a few more days, nothing happens, start over and place the culture in a different part of your home.