In a high-rimmed jar, mix together the 100 grams of flour and 100 grams of water. Once combined, the flour and water will be thick and resemble a very thick pancake or waffle batter. Cover the jar with a cheesecloth or small towel and secure the cloth over the jar with a rubber band.
Your work is done for now. It's time to wait and let the natural yeast (bacteria) do its work and bring your starter to life. I recommend placing your starter near a fruit basket (on the counter) or if your home is cold put your starter in the warmest location of your home.
After about 1-2 days, you should notice that your starter looks and smells different. It may have a slightly sweet and sour aroma, air bubbles may appear in the starter, and the starter has risen. The starter will also change from a thick and hard-to-stir to batter to one that's a bit more pliable. You're not looking for any kind of crazy WOW changes, just slight changes here.
Discard 50% of your starter.
Feed the sourdough starter with 60 grams of fresh flour and 60 grams of filtered water (it's important to stick with the same flour for your starter versus change things up). Stir the fresh ingredients into the starter, place the cheesecloth (or towel) back on the jar, and secure the cheesecloth or towel with a rubber band. Place the starter back on the counter (near a fruit basket or warm spot, if possible). Continue to do this for 4-7 days.
Once your starter is mature (around 5-7 days after starting and consistently feeding it, depending on the temperature of your home), you'll notice that it grows and shrinks throughout the day. Growth happens after you feed your starter with flour and water (and discard half of your starter before doing this)--growth usually happens during the first 2-12 hours of a fresh feeding. It's ideal to feed your starter when it shrinks back down as this means it's ready to fed again (it's consumed all the food you gave it and now it's ready for more so it can grow again). The more you feed your starter (between 1-2 times a day, depending on the current temperature in your home as warmer weather can make for a lively starter while cooler temps so it down), the healthier and more active it will be. When it rises (roughly 2-12 hours after feeding), this is considered an "active and bubbly or freshly fed starter" and it's the ideal time to make bread dough. You can use the discard starter (what you toss each time you feed it), to make waffles or pancakes or crackers.
To Maintain an Active Starter (AKA: Keep It Alive):
Once a day, refresh your starter by feeding it with fresh flour and water (60 grams each). If your starter is super active (rising and falling often), you can feed it twice a day.
If you're not going to regularly bake bread, you can keep your mature starter (it's been alive and healthy for a couple of weeks now) in the fridge. To do this, at feeding time, discard 50% of the starter (remember, you can use this to make waffles, pancakes, or crackers if you want), feed the starter with 60 grams of water and flour, and cover the starter. Let the starter sit at room temperature for an hour and then place the starter in the fridge to hibernate. This is also a good way to keep your starter alive if you're going to be traveling and won't be around to feed the starter on a daily basis. There's no need to feed the starter until you pull it back out of the fridge because you're ready to start baking bread again. The starter doesn't need to be fed while it's hibernating in the fridge. I recommend feeding it once a week, if possible, when keeping it in the fridge. You'll need to pull the starter from the fridge at least 1 day before starting the sourdough bread process, discarding 50% of the starter, giving the starter a fresh feeding (60 grams of flour and 60 grams of water), covering the starter, and placing it back on the counter in a warm spot.
I've had the most success using whole wheat flour to make and maintain my starter. Plus, whole wheat flour is pretty inexpensive, which is important to me since I'm discarding and feeding my sourdough starter on a daily basis. I personally don't keep my starter in the fridge, because I usually bake bread 1-2 times a week and don't mind the regular feedings. I keep my starter in the fridge to hibernate when we travel, or during busy seasons of life when I won't be able to regularly feed my starter and make bread. Now that my starter is mature and thriving, I don't actually weigh the 50 grams of water and flour each time I feed the starter. I know, just from eye balling it and using a 1/4 cup measuring cup, what my starter should look like when it's fed. Once you get to a point of regular feedings, you'll get to know your starter and the ideal feeding appearance and consistency very well--so don't feel like you need to use the scale for this once you're a pro. You will need a scale for the initial starter creation and each time you make bread, because weight measurements are far more accurate than volume measurements. Now that you have a starter, you can make sourdough bread. A Sourdough starter can also be used to leaven more than just a loaf of sourdough bread. You can use a sourdough starter to make sourdough waffles or in place of the leavening agent (i.e. baking powder) in quick bread recipes. It can also be used to make pizza dough. Google is a wonderful resource for recipes. For troubleshooting (mold, etc.), Cultures for Health is a great resource. I recommend checking out this article.