To get started, it's helpful to read everything you can find on the subjects of animal communication, psychic ability, and intuition. Also read my book, Learning Their Language and try out the exercises. Once you've learned the basic techniques of animal communication, you will have to practice regularly if you want to build your skill and confidence.
If you don't have the time to read or access to a class, you can still improve your communication and relationship with your animals by changing the way you think about them and the way you talk with them.
Changing Your Beliefs
I've been an animal-lover all my life, but until I studied animal communication, I didn't realize that animals are truly able to understand everything we say or think to them. They understand our spoken words just as well as another human would, and since, unlike us, no one taught them they weren't intuitive, they can hear everything we think to them or about them. They also feel everything we feel and can see the images we form mentally. If you want to be successful at animal communication, you need to try out these beliefs, which are, admittedly, completely different than anything we've been taught about animals or about how life works.
As an experiment, spend two weeks talking and thinking to your animal as if he or she can understand you perfectly. This does not mean your animal will turn into an obedient little robot, anymore than you or I would in the same circumstances. Your animal will simply "get" everything you say or think. Try really believing this for two weeks and see what happens. While you're at it, change any outdated beliefs you may have about animal emotions. Animals have the same emotions in the same intensity that we do, so work on trying out that belief as well.
What I expect you'll find by doing this experiment is that your animal will be more attentive and interested in you, respond to what you say and what you ask for, and show you, through behavior, that he or she understands every word you say. It's a great experiment and it doesn't cost a thing to try it.
Talking with Your Animals
As another experiment in improving your relationship with your animal try a talking experiment. Pick a regular time to talk, once a day or once a week. When you talk you can discuss anything from specific issues between you and your animal to whatever is going on in your life in general.
Speak from your heart, as if you are addressing another person who is your equal. Explain how you feel about an issue, discuss and negotiate, ask for your animal's advice and cooperation. If the normal routine is going to change, or if you're planning a trip, explain all these details so your animal won't have to guess at or wonder what is happening. This can be especially helpful for animals that have separation anxiety.
Before you finish your talk, take a moment to close your eyes and ask your animal if he or she has a question for you. If a question pops into your mind, no matter what it is, just answer it as best you can and assume it came from your animal. By not questioning the question you give your animal a chance to get through to you. If you don't get a question, just say, "OK, I'll ask again later," and try it another day.
Try these experiments and see if you notice a shift in your relationship with your animal. You may find that these few small experiments will influence the way you relate to all animals and nature in general.