1. It's a problem of getting from one place to the other.
Offer to do anything that will save the person steps. Moving on crutches is more tiring than it looks. Not only is it involving muscle groups in new ways, there is pain, and, as you know, pain is exhausting. Offer to sign them in, get them a cup of coffee, pick something up off the floor for them, get them seconds, give them the closest seat, bring the phone to them.
2. Hands are on crutches. Hands are therefore not free to do anything else.
The first thing you learn when you're on crutches is that you're finally there and you can't take it back with you! (Thus you start wearing things with pockets.) You can help by opening doors, offering to carry things, press elevator buttons, put things in bags for them with handles they can drape over their arm. Offer to carry it to the car for them. Open the car door for them when you get there.
3. Balance is precarious. Ask how you can help, don't just rush in.
Then listen. A strong arm is very useful to lean on and far more reliable than a crutch. Grip the person in the way you feel most secure and rely on some guidance from them at the same time.
4. Offer to run errands for them.
Any and everything. If you're going out, give them a call. A simple, "I'm going to the grocery, need anything?" is all it takes. If they live alone, imagine how helpful this is. If they live with another or others, the workload has still been increased significantly on all concerned and their lives have been disrupted.
If the person lives alone, and you're a neighbor, think of things like bringing the mail or newspaper to the front door, walking their dog, or watering their lawn.
5. Share your own stories.
Anyone who breaks something generally feels a little foolish for having done so. Since breaking my ankle I've heard story after story of "it was just a little stone" or "I just stepped off a curb wrong" that made me feel more "normalized."
6. Offer to help them up from their chair.
Strong arms pulling you up are much more reliable than using the crutches. It also saves energy, and removes any chance you'll put pressure on the injured limb accidentally and cause pain.
7. Do not distract them during the hard job of moving from one place to another. It is hard work and takes constant vigilance.
A person on crutches must be looking at the walking surface constantly -- the floor surface (marble, cobblestone), rugs that might move or curl, any spills on the flooring, obstacles, anything that might hit the damaged limb and cause blinding pain, anything small and furry that might move and trip them...
8. Make it possible for them to elevate the foot or leg.
Move a chair or table around for them, get up and move yourself. It throbs as soon as it turns downward.
9. Ask them about the temperature of the room.
We dread sweating, because... if you've ever had a cast, you know why, which brings up point #10.
10. If it's happened to you, say so, and then ask to help.
It's particularly comforting for someone to say, "I know what it's like, so please let me ..." And also share what you've learned. The learning curve doesn't exist. It was someone who'd been on crutches herself who pointed out to me that mine were set 4" too low.