First decide whether this fledgling actually needs rescuing
A fledgling dove — mostly feathered, short tail, able to grip and hop — normally spends days on the ground while its parents continue feeding it, and removing a healthy one does it harm. Watch from a distance for a good while: if it is alert, feathered, and a parent visits, leave it, moving it only a short distance to a safer spot under cover if it sits somewhere exposed like a path. Intervene when it is clearly injured, cold and fluffed with eyes closing, covered in flies, has been caught by a cat, or when you have watched long enough to be sure no parent is attending it. A naked or barely feathered nestling found below a nest is a different case again — returning it to the nest, if you can reach it safely, beats any box.
Make a shelter that is warm, dark, and boring
Line a small cardboard box with a soft, non-looped cloth the bird's feet cannot tangle in, add air holes, and place the fledgling inside with as little handling as possible — clean hands or soft gloves, supporting the body without squeezing. Put the lid on: darkness is calming and stops escape attempts that injure wings. Keep the box indoors in a quiet room away from children, pets, television noise, and kitchen fumes. Resist checking it repeatedly; every peek is a predator event to a wild young bird, and stress alone can kill a borderline fledgling before help arrives.
Warm it slowly and from the side
A chilled fledgling cannot digest or respond well until it is warm, but overheating is just as dangerous. Use gentle, indirect heat: a warm-water bottle or heat pad on its lowest setting placed against one side of the box or under half of it, so warmth radiates in and the bird is not cooked from below with no escape from the heat. The box should feel comfortably warm, not hot, and the heat source will need refreshing as it cools. Never use a lamp shone directly at the bird, and do not warm it against your body while doing other tasks — steady, quiet, contained warmth is the goal.
Do not feed it or give water while you wait
This is the hardest instruction to follow and one of the most important. A cold, shocked, or injured young bird given food or dripped water can inhale it into its airway, and doves have specific feeding needs — parents produce a special food for their young — that kitchen improvisations do not match. Keep the mouth closed and your kindness directed at warmth, shelter, and speed of contact with experts instead. The exception is only what a vet or rescue tells you to do on the phone for this specific bird, in which case follow their words exactly rather than general advice from the internet.
Make the call count and hand over well
Phone an avian or wildlife-experienced vet, or a licensed wildlife rescue, as soon as the bird is boxed and warm, and describe what they will ask: where and when you found it, whether a cat or window was involved, its feathering and alertness, and whether parents were seen. Note their advice and the time you called. Arrange transport promptly if they ask you to bring it in, keeping the box covered and the car quiet. If anything about the bird's breathing worsens while you wait, call back rather than hoping. While those calls are under way, KinsLe's Kinny draws his answers to follow-up questions from this Answers library in KinsLe.