How do I thicken soup broth?

For egg drop soup, add cornstarch as others have suggested. For other soups, I would try grated potato, orzos or other smallish pasta shapes, or oats (yes!) or other grains. Since I am a vegetarian, these are my go-tos for thickening.

Adding a potato to simmering broth helps. (You can strain it out, or not, depending on what the final product is.) A bag of frozen peas can also add starch, and sweetness. These are good alternatives if you don't want to get your thickness from meat products. They can also supplement meat bones, if you are using them.

Egg drop soup: You thicken it with cornstarch and water..add it to the broth and heat until it thickens.

I found the dropping the eggs into egg drop soup a problem when making in small batches--too many big clumps.
Use a bowl and hold down a fork over the bowl with your thumb and slowly tilt the bowl so the eggs run down the tines of the fork. (or two chop sticks if you can). So you get a very slow stream and whisk at the same time as it drops in.

a few little tricks can give you a thicker, creamier base without actually adding any cream. you can add some rice or some beans and blend it thoroughly to make a thick broth before you add the rest of your ingredients

Cornstarch will get you the consistency of egg drop soup. Just make sure you first mix it with some water before dropping it into boiling broth, or else it won't work.

All of the above is true, however broth, by it's very nature, is meant to be thin -- watery when hot.

More chicken and or more bones will give it a thicker, more gelatinous quality. So will simmering longer. Either will also give you more flavor as well.

You could reduce your broth so it's thicker and more concentrated before adding it to your soup. Or you could use homemade chicken stock, which will be thicker and more gelatinous...a little more work but always nice to have on hand!

There are several ways to thicken soup - most involve starch. Adding some flour as in a roux or a potato will usually do the trick. If you're going for egg-drop soup consistency, a wee (and I stress the wee part) bit of xantham gum will do the trick.