So you want to thicken something to turn it into a sauce. Here are the basic ways.

1. Reduction. this means you just cook your liquid down until it naturally thickens. This doesn't make very much sauce and you want to be careful because the process accelerates towards the end so it is real easy to reduce your liquid to the point that somebody notices something is burning. There is no way to rescue burned sauce.

2. Flour. This is the basis for gravy type sauces. Mix flour with butter or oil Not water. The classic way is to mix butter and flour in equal parts and cook it on medium until it starts to get darker, this is called a Roux. Make it as dark as you want your sauce to be, although it can take awhile. It adds thickening, color and tremendous flavor, however the darker it gets the less thickening power it has. Once done, let it cool before stirring it into a sauce to thicken it. Or, add liquid to the hot Roux. The best way to incorporate roux is with a whisk. Cooking the sauce after adding the Roux improves the taste. If you are in a hurry mix some oil and flour together and stir it into the liquid and cook to get rid of the raw flour taste.

3. Cornstarch. This makes a translucent sauce like a glaze. Chinese food is an example. Mix cornstarch and water 1:1 to make a slurry. Stir it into simmering liquid a little at a time to thicken, you will see it turn from white to translucent. You don't want to cook it for very long because it will start to break down.

4. Pasta water. The start in a cup of water from cooking pasta can provide small amount of thickening.

There are a host of other methods but if you remember flour:oil or corn starch:water you will be et for just about anything.