Start noticing what your pet is paying attention to. What interests them and what's their reaction.
Start noticing your pet's facial expressions when you are talking to them. Relate that to what you've learned about reading other's faces to see what they are saying in their expressions. (Remember, babies can get their wants and desires across to their mothers and fathers with out crying out.) It's the beginning of communication.
Quiet your mind center yourself or learn how to meditate. It will quiet "the committee" in your head that try to check and recheck and triple check then categorizes the information that goes in and out of your thought process all day long. It will help you to detach from the, so called, logic override in your speech so you can speak to and for the animals.
Gently reach out and ask a simple question in your head. Is this question your issue or the pets? Be simple with it. Don't expect a complicated lengthy answer.
Allow the FIRST thing that comes into your mind to be verbalized by you. Then see what your pets reaction is. You might be surprised at their facial or vocal answer.
Don't think about, "Is this real?", "It can't be that!" Just try and observe your pets answer, facial, body, and vocal. Be detached from the outcome.
Try the new information out. See if it's a viable answer or if your pet has a sense of humor. Sometimes they will try and interject some humor when we take ourselves too seriously. Be light with it. Animals often feel humans are too serious with questions.
Now, have some play with your pet and lighten up. Practice talking to your pet about everything, like you would your friend or child. Love them. You can sing made up songs about them. Have fun!! Include their input in your household decisions. Keep it easy so then will feel free to come to you if something big is up for them.
Allow them their independence. No one likes to feel that their thoughts are constantly listened to, or that someone is trying to intrude into their space.
Practice and be easy with the questions and your intuition. No straining or you'll miss the meaning. Remember they "talk" to each other all the time without vocalizing. It's us, humans, that think we have to make noise to talk, not the animals