This is a really big question because there are so many invertebrates. There may be well over a million species. There are a few big ideas that help in explaining this, though.

First, if something is small and surrounded by water, some wastes can just leave the body by a process called diffusion. Diffusion means that things tend to move from where there’s a high concentration to an area where there’s a low concentration. This happens just because molecules are always moving, so they sort of wander away from where they start.

When you put food coloring or lemonade powder into a glass of water, it spreads out by diffusion. Eventually, the coloring or powder will spread out over the whole glass, but if you don’t stir, it will take a long time.

Diffusion is very slow, so it only works if there’s not far to go. If an animal is very small, or very flat, this works because no cell is very far from the outside. Animals that are bigger need a way to move things faster. They have liquid that moves around in their bodies, picking up waste. They may have some way to pump this liquid, or it may just get squished around as they move. The fluid may move in tubes, like blood vessels, or just be in the open spaces in the body. They usually have an opening to allow the liquid out. Bigger invertebrates are more likely to have pumps (hearts) and tubes (arteries and veins) for moving the fluid. They are also more likely to have organs to process the liquid waste (kidneys) and tubes to carry the waste out of the body.

For solid waste, most animals have an opening at the end of their gut to let the waste out. But there are other animals, like sea anemones who have one opening that acts as a mouth for food to go in, and an anus for waste to go out.

Some invertebrates are huge. The giant squid has an eye as large as a dinner plate. The invertebrates that live on land don’t get very big. Can you think of any reasons why? Hint: Invertebrates don’t have bones. What do they have?

I found information for you on a site and the Encyclopedia Brittanica:

In most unicellular organisms, excretion is a simple process of diffusion into the surrounding medium. In other organisms, contractile vacuole may also help in excretion. In sponges and coelenterates, waste is diffused through epidermal cells to the surrounding water or into the canals and through gastro vascular cavity by the en- dothermal cells. In flatworms, there are definite ex¬cretory organs, the flame-cells (protonephridia) which discharge the waste outside.

In annelids, there are tubular excretory organs called nephridia to remove the waste matter. Insects have many malpighian tubules or renal corpuscles which pick-up waste sub¬stances from the body of diffusion and pass them into the digestive tracts. In other arthropods, especially the crustaceans, the excretion is performed by a pair of antennary or maxillary glands. In echinoderms, excretion is performed by amoebocytes, or mobile cells which move like amoeba.

So far as they have been investigated, the invertebrates in general conform to the principles applying to all animals, namely, that aquatic forms get rid of ammonia by diffusion through the surface of the body; terrestrial forms convert ammonia to uric acid. This implies that in aquatic forms the excretory organ is principally of importance for the composition of their body fluids.

Invertebrates excrete wastes in basically the same way that vertebrates do. However, *most* animals, vertebrates included, have separate ways of disposing of waste produced by burning proteins (urine) and waste that has passed through the gut (feces), and in some invertebrates, the organs are *very* different from those of vertebrates. How different they excrete their wastes depends on one invertebrate to another.