Whenever you are boiling something, you need to consider why you are boiling it.
The commonest and most obvious reason is to hold the stuff that's floating around in there at around 100 degrees centigrade, causing them to cook.
Another reason is to drive out water as steam, making the dish thicker and the flavour more concentrated. This is called reducing.
Which of those you're doing, dictates how you go about it. If your intention is to reduce, then you'll want the soup at a rolling boil, because every bubble represents some water being driven out. Cook on full heat, and watch carefully. It doesn't take long to lose a lot of water this way -- and eventually it will dry out so much that it sticks to the pan. And it will fill your kitchen with steam. There will be condensation rolling down the windows on a cold day.
If you don't intend to reduce, then any bubbles you see represent a waste of energy, and you don't want to lose water from your soup as steam. So get it boiling, then turn the heat right down, and put a lid on so that steam is caught in the lid and drips back into the soup. You want some very gentle bubbling, just to reassure you that the soup's at around boiling temperature.
With experience, you'll be able to get a low simmer easily.
It might be worth investing in an electric slow cooker; simmering stuff gently is what they do best, and they're really cheap now.
Two other things that might thicken up your soup:
- Dry ingredients absorbing water -- e.g. pasta or lentils. You just need to add enough liquid to hydrate these ingredients.
- Thickening agents such as flour -- either use less/no flour, or add liquid to compensate.