In the book, The River Why, a man hooks a salmon with a 3 lb. test line. This is light enough to break with any resistance. He follows this salmon all night feeling the energy of the salmon through this tenuous filament. The salmon gets used to his presence, so used to it that he can enter the water and pick it up, should he choose. For the man, it is a spiritual experience.

I've had spiritual experiences with my horse, following him around the pasture, looping left and right as he turns and faces, and stops and decides whether I can come closer or whether I'm just fine right there.
Mostly I can walk up, touch his shoulder, say hello, groom at liberty. This all changes when the farrier comes. Ed likes his farrier. She's kind and gentle and pretty quick. But Ed is not a fan of the pedicure. And thus, our game of catch is far more difficult.
The energy technique that I use to catch Ed is also good for catching any pet who needs grooming or medicine.
The first thing that's important is this mindset: you have all day. If there is any outside chance that you will give up on catching your pet, you've already lost. A smart pet will wait you out.
Secondly, Don't over-identify with your pet's potential discomfort. If you think, "Oh my poor baby needs to get a shot today!", your cat will not come out from under the bed. Instead, think, "This is a necessary part of life, and it's going to be okay." (Because it is and it is).
Third, approach your pet in a way that doesn't signify you're a predator. Pet brains will always pick up on predator behavior. For horses, this means that I can't walk straight up to Ed. Instead, I walk in curves, s-shapes. I walk with gentle determination.
I feel for Ed's energy. I get him just to the point where he's going to take off, and then I stop and back off. When his energy dies down, I take a step closer, and wait. Slowly, we get to the point where he's comfortable with me touching his shoulder, and neck. Then he's ready to be haltered.
For cats and dogs, I usually walk into the room that they're in, shut the door and sit down. They approach and as soon as they get close enough, I pick them up. If they're not coming close to me, I settle in a few feet away.
Again, it's important to keep a gentle and loving, but determined mindset.
Also, do not hurry. Hurrying creates urgency which creates a sense of panic. Every healthy creature avoids panic.
I know that as soon as I post this, someone is going to ask, "Hey, how does this work with my dog at the park?"
Getting your dog to come to you at the park is a combination of last week's
Tuesday Training and this one. Your dog has to know to pay attention to you first. Again, if there is any chance in your head that they will get to stay and play, they're staying and playing. :)
I hope this helps you today!