Both .. .. for a safe practice tool, roll up a pair of socks, tie a string to them, make certain there is enough string to be as long as your sling. Whirl it over hand and throw, whirl underhand and throw, whirl like helicopter and throw .. .. one of the orientations will probably feel best.. ..the whirl shouldn't be too fast ...just enough to let you feel where the sock is in its trajectory. When you can hit a target with your sock consistently you will be surprised at how much your rock slinging is improved too.  

P.S. this is a some what safe indoor practice routine you can use in a small room.

Funny how individual slinging is. I always get heaps more power with overarm but found basic accuracy with underarm easier. As you give no details of your sling it's hard to be specific but underarm shots which go straight up means the release is too late. Possible causes for this include,
a. the sling is too short (for underarm I like a sling which is approx. from the waist to the ground)
b. the pouch grips the ammo too securely (make sure there are no snag points, cords not tangled etc.)
c. the ammo is too light (IMO anything much lighter than a tennis ball is too light to sling effectively, it's hard to "feel" it and it doesn't have the weight to open the pouch on release)
BTW I second any suggestions to use tennisballs. Great for beginners, safe and consistent.

And of course there is the minor matter of technique. There are quite a few videos on YouTube that show slinging. For a good relaxed underarm style one of my favourites is "Lampi100". Search under his name. His videos are always self-taken and show only a rear view but they are very clear and easy to emulate.

Hope this helps.

Horses for courses again! I love Fig.8 and use it almost exclusively. I find that the release knot always hits the ground on follow through. In wet weather the sling always gets muddy. In fact in my favourite slinging spot in my backyard there are two bare patches where the grass has been worn away, one from my feet and a smaller but definite one foward and slightly to the left, where the constant whipping of the release cord has also killed the grass.

With underarm there is some risk of hitting the ground with the actual pouch, especially if the sling is too long but the release cord has lost all its velocity by the time it touches the ground.

In the guides and articles section of the main site there is this how to for slinging the fig-8 by Mark Weaver http://slinging.org/index.php?page=tennis-overhand-weaver-style-overhand-release...
There are also several videos on youtube of slingers doing the figure 8, such as this one
http://www.youtube.com/watch?v=8orcxkmtRnc&feature=related
this one
http://www.youtube.com/watch?v=sKY8g-pPmi4&feature=related
and one that I did
http://www.youtube.com/watch?v=d-yvC5f1SWw

I'm not sure that I'd say overhand is better... I use it for most of my slinging, but it really comes down to what works best for you.  That could be overhand, underhand, sidearm... all kinds of styles out there.  Try them all, and see which you like best.

In my opinion, 20-30 yards is pretty close range, and so, I would use the overhand method in that case. I tend to reserve underhand for tossing at massed objects or trying for distance. Others, I know, do it differently. To each their own, I suppose. I find that at such close range, for me, the stone seems to stay level longer with the overhand throwing, meaning I'm less likely to overshoot a closer target using a sidearm or overhand throwing method.