This is what I do with calves that are a manageable size (less than 300 pounds or so). I get calf and momma in the barn. Separate mom from calf (mom in another room of the barn where she can't get me). I lasso the calf with a rope (don't forget your leather gloves!). I am not a cowgirl...I just chase the calf around until I can get the rope over it's head, then hang on. I can generally hold my ground by holding the rope around my hips and using my body as a post. Once the calf settles down a bit, I get the rope around a post or through an eye-bolt and reel him in. Tie him up short and you can have a look.
Another way is to simply grab him and flip him. Grab the front leg near the body and grab a handful of skin in front of the back leg and heave him up and over on his side. Sit on him and have a look. I can usually flip them for the first month or so. Again...confine mom so she can't come get you. I have never been able to hog-tie a calf well enough to make it work, but a rope around one leg can keep him on the ground or put him back there in short order.
In this case, I would tie the calf so you can get some water on his foot to see what is going on. Many times a foot will start oozing after 15 minutes of water on it and you can tell if it's infected inside (foot rot) or find an offending foreign object. Also check the whole leg for a knots, heat, etc. I had a calf who broke his leg at about a month old. He had a huge swelling between the knee and foot, but could still run around on three legs. No treatment possible, so I just kept him and mom in a small pen so he didn't have to travel far for dinner. He recovered, but it took months! Despite his handicap, he was a bear to catch!
Jena