Communication is a two-way street. Animals are already masters at this, so they are sending you information all of the time, even if you don't recognize it as that.
Maybe that "intuitive sense" you have about what an animal needs or wants is not coming from you, but from the animal — and you are intuitively picking it up! No, it may not sound like a typical conversation, but it's communication nonetheless.
Further, animals are also always picking up messages that you unconsciously send — which means at some level, you already know how to do this.
With that in mind, start consciously sending messages to the animals around you. And consciously listen for them. Since you're probably already communicating, you might as well be aware of it and enjoy the process!