How to build independence

My LO is super dependent. Yes I know he's a baby. But he needs attention all the time. Rarely will he be content to sit and play by himself (with adult supervision in the same room). Any tips or tricks to help him build independence?

I think the problem is, my husband and I just love playing with him so we are always playing and interacting and he loves it. But it makes it tough especially if someone else it watching him. If he doesn't get that constant attention he starts crying or getting angry.