Are you talking about edit mode or object mode? In edit mode, you always edit one ‘object’, so any new polygons are still part of that same object (even if they don’t touch). You can use L (while hovering close to a shape, also try Ctrl-L if you have one or more vertices selected and don’t want to worry about hovering your mouse over a vertex) to select all connected vertices, and you can use p to separate the selected vertices to a new object.
In object mode, you can only select whole objects. You can use Ctrl-J to join two objects into one. Switch between modes using the Tab key.
I hope this helped, I’m assuming that’s the problem. There are a ton of ways to manage things in Blender, to make it easy to produce complex animations, so maybe you are having some other problem.