I'm a pretty skinny guy, and I've been weight lifting, working out, etc, and I've noticed some results with my upper body, but I'm as chicken-legged as ever.
So, what are some good, rather simple home exercises to work out the Calve muscles?
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You can do standing calf raises by going on your tip-toes and then flat. You can do them on the floor or for a greater extension use stairs to get a deeper flex going down (i.e. heel lower than toes). You can carry dumbbells but for stability and safety reasons, I would suggest doing those on flat ground and not on a step.
You can also do a seated calf rise: http://www.shapefit.com/calf-exercises-barbell-seated-calf-raises.html
you can substitute bands for the bark or any weight on your legs. It sounds like you're focused on your legs and not just the calve muscles...which makes sense, since isolating a single muscle isn't always the best approach (since various muscles work together). What I would really recommend is doing squat exercises, either with or without weights.
Here's a link to a body weight squat example: http://doubleyourgains.com/how-to-do-bodyweight-squats-and-hindu-squats
and a pic of a prisoner squat:
As unpleasant as they are, good old squats are about as good a way to grow your legs as anything.
Calf raises are not likely to make your calves bigger if you're predisposed to skinny legs. Of course, if you are so predisposed, you're going to be at least partially out of luck. But the only time in my life I haven't had chicken legs is my senior year of high school when I was doing lots of squats, stair running, running up the stupidly steep hill by my school, etc. And even then my biceps were almost as big as my calves.
So the answer may just be lots of squats and weighted calf-raises.
I also had small calves at one point. I started walking around as if doing calf raises to make my muscles work more. On long walks I usually do this until they heat up, then repeat after then cool down. I avoid taking them to the point where they are painful; feeling like I've had a good workout is sufficient.
Before I started this I could palm my calf and nearly touch my tibia with both my thumb and middle finger; these days I can barely clear the muscle with my hand.
Unfortunately since I started this without guidance, I don't know the potential for overworking the muscle.