How you know an egg is likely stuck
A hen with a bound egg usually stops looking like a hen going about her day. She may stand upright in a strained, penguin-like pose, her tail pumping up and down as she pushes, or sit in the nest box for long spells without producing an egg. Many go quiet, lose interest in food and pass few droppings, because the stuck egg presses on everything behind it. If you pick her up gently and feel low over her abdomen you may be able to feel a hard, oval shape, but handle her only briefly and never squeeze. Straining can have other causes too, so treat these signs as a reason to act and let your vet confirm exactly what is happening.
First move: bring her in, warm and quiet
Move her off the perch and away from the flock into a box or crate lined with an old towel, set somewhere warm, dim and free of draughts - a utility room or bathroom works well. Warmth is not just comfort here: it helps the muscles of the oviduct relax, which is exactly what she needs to pass the egg. Offer her water within reach, since a hen that has been straining may be dehydrated, and then leave her in peace for a while. Quiet and darkness also switch off the urge to keep laying, which rests the whole system while you phone the vet and arrange transport or a visit.
The warm soak, done properly
Fill a basin with warm water - comfortably warm to your wrist, never hot - deep enough to cover her vent when she sits in it. Lower her in slowly, support her body with one hand so she feels secure, and let her soak for fifteen to twenty minutes. Many hens relax visibly in the water, and some pass the egg during or just after a soak. Lift her out, pat her dry so she does not chill, and settle her back in the warm box. You can repeat the soak after a rest if your vet agrees while you are waiting, but keep each handling episode short and calm.
What not to do while you wait
It is tempting to try to free the egg yourself, and this is where hens get hurt. Never press or massage her abdomen towards the vent, never probe inside the vent, and never try to break the egg to collapse it: a shell that breaks inside her leaves sharp fragments and spilled contents that can set up a serious infection. Do not put her back with the flock to see how she goes, because flockmates peck at a bird showing weakness, and do not let a brief improvement talk you out of the vet call - a hen can rally for an hour and then go downhill fast.
When this stops being first aid
If she has not passed the egg after a couple of hours of warmth and soaking, if the straining is constant, or if she becomes weak, fluffed and closed-eyed, this is an emergency rather than a wait-and-see - travel now, keeping her warm and in the dark for the journey. The same applies at once if tissue protrudes from the vent or her breathing looks laboured. Your vet can examine her, feel for the position of the egg and support her strength and calcium levels while helping the egg out safely. For anything still unclear while you wait, put a follow-up question to KinsLe's Kimmy; she answers using the KinsLe Answers library.