There are many ways to connect with an animal. And there are good ways and there are bad ways. In order to connect well with an animal, consider the following ideas.
Remain calm around new pets or animals. Animals sense fear, anger, annoyance, uncertainty, etc. While you might think you have these emotions under control, unless you really do, you will release bad feeling through your body movements and presentation. If you're upset, fearful, etc., wait until the feelings pass before approaching and interacting with a new animal in your household or farm.
Keep new animals away from existing animals until they are properly settled. It's hard enough coming to a new home without having bossy or inquisitive animals pestering the new animal. Give the new animal some space and time before allowing it to gradually interact with the existing animals. You should always be around for the initial encounters unless something goes wrong and you need to intervene quickly.
Involve your pets in your life. Animals enjoy being a part of your activities; get used to their presence and don't yell at them, or kick out at them, etc. If they're in the way, simply pick them up gently and put them in the yard or another room until you're finished with your activity. Spend a lot of time playing with your pets, loving them, and generally talking to them.
Don't be speciesist. Build trust and respect with your pets and animals; we're all animals and other species communicate with us and vice versa through love, mutual respect and provision of attention. Another key element is to cease the idea of "ownership" of animals. We have animals in our lives and we are responsible for them but we don't "own" them any more than they "own" us or we "own" our kids!
Read and learn. When you have animals in your life, it pays to know as much about them as possible. Never stop learning. Read books and watch documentaries about animals to learn what you can about them and their way of understanding the world. Work your knowledge into your handling methods so that you become a better communicator and connect closely with the animals in your life.
Dogs you are familiar with like to be looked at in the eye.
Young dogs like to play and chew so make sure you have some chew toys.
Don't ever harm an animal.
Stray dogs or any other dog that isn't yours, don't like to be looked in the eye because they consider this a challenge and that may provoke them to bite you.