In general, we can say that they are simple organisms composed of one cell, or grouped together in colonies, or as organisms with many cells, sometimes collaborating together as simple tissues. Most algae form some sort of spore, which is a cell that is often motile and serves to reproduce the organism. Algae also have sex, often a very simple kind of sex where the algae themselves act as gametes, but sometimes very complicated with egg and sperm-like cells. Algae of one kind or another have been around for more than 2 billion years. We are still discovering new algae, sometimes whole groups of them at a time.
Seaweeds are algae that liven in the sea or in brackish water.
Red and brown algae are almost exclusively marine, whilst green algae are also common in freshwater and in terrestrial situations.