Everyone has their own methods for halter-breaking cattle/teaching them to lead. From my own personal experience, it is easier to train a calf to lead once it is a bit older. We train all our heifer calves to lead, and start working with them between 8-10 weeks, sometimes a bit later.
I would not recommend putting a halter on an animal with a short rope and letting it walk around. Not saying it wouldn't work, but you'd be surprised what kind of trouble any animal can get into with even a short rope.
I would recommend tying the animal with it's head up high (with 10-12" of rope free at most, less would be better). An ideal place to do this is if you have a pole shed, one of the poles. I'd start with a couple hours tied up, and I agree that it is best to stay there, (1) to see that she doesn't get in any trouble; and (2) so she associates you/person with the halter. When you let her down, you might want to leave her still tied up with the halter with perhaps 24-30" of rope and offer some hay and water. Two or three sessions like this and most animals are ready to lead.
One thing to remember is that even a small animal is stronger than most men, so fighting with them is generally a losing battle. You also don't want to reinforce the idea to the calf/animal that the halter is associated with resistance, fighting the lead, etc.
After these first three sessions, it is important to work with them regularly. If you have the time, lead them three or four times a day for 10 or 15 minute sessions. That's how often we would work with our Holsteins we showed. Similar to the show ring, I like to lead cattle walking backwards -- you have much more control. Do make sure to hold the animal's head up while leading, again you have more control and it's consistent with showing. Yes, you'll be walking backwards, but you should have your left hand on the halter where the muzzle rope and neck rope meet right next to the cinching loop, and then hold the free rope in your right hand. You want the animal to respond (stop) by pushing back slightly with your left hand. While leading the animal backwards, you can slow any desire to go to fast or veer by forcing the animal's head up, or putting your left hand on the left side of the animal's face holding the halter and placing the right hand where you'd normally hold your left. If the animal does not want to move from a stop, turn her around (clockwise) and she should move. You don't want to reinforce this jerking/pulling on the halter.
As you work with her regularly, work on stopping and starting, varying the speed with which you lead the animal, turning, and even backing the animal up. With regular work and with time spent grooming the animal, she should be leading proficiently in a couple weeks.
Your behavior around the animal at all times is important in developing good behavior in the animal. Consistent in your approach, firm (animals can sense who is in control), and calm (no yelling, sudden movements).
Things not to do:
(1) Don't try to train an animal to lead with dogs around, kids zipping by on bikes and shouting, etc.
(2) Don't fight with the animal, and it doesn't do any good to slap the animal's muzzle with either hand or rope or any other kind of pounding on the animal.
(3) Wear good work boots, don't be running around with a pair of flip-flops.
(4) When leading an animal, don't let the animal have her head and 5'-6' of rope. If anything happens to spook her, you won't be able to control her that way.
Good luck with your calf.
