1.  Put your sling on, shoulder fabric cupping your shoulder, rings positioned between shoulder & breast. Pick up your child.
2.  Get a good grip on your child's legs and back, supporting the neck of very young babies, and hold the child against the shoulder without sling fabric .  With larger babies, you will be tipping the child over your shoulder, great fun for easily amused toddlers.
3.  Place your baby's body in the sling, pull the sling body fabric over the baby's bottom as you thread the baby's legs through the sling;  with smaller babies, you may keep their legs tucked in the sling, squat position.  Active, curious babies may be faced outwards(kangaroo-style.)  Sleepy, upset, nursing, or along-for-the-ride babies are placed tummy-to-tummy.
4. Hold the sling body and baby with one arm, get a good grip on your rings, and scoot the baby and sling so that the baby rests over your navel or there abouts. The baby's bottom must be firmly seated in the sling and there should be enough fabric on the baby's back to hold the child in place if he or she tips away from your body a bit.  You want the fabric to spread all the way to the back of the baby's knees, too.  If the ring sling feels too loose, then lift up the rings to adjust it. 
5.  If your baby is small but strong, you can use the tail of the sling to pad the tummy-to-tummy carry hold. 
Leah's thoughts on this postion:
A sling makes a baby's weight feel much less significant.  Babies faced inwards, tummy-to-tummy, take long naps while the babywearer has hands free to do other things.  When awake, the same baby can nurse or explore the babywearer's face and garments.  Babies faced outwards have a novel view of the world to keep them entertained.

Tummy-to-tummy is an excellent position to nurse from.  Use your sling tail as a cover-up.

Try wearing the sling with the rings on your back.  There are interesting variations possible this way.

Tummy-to-tummy is a hit with babies of all ages.  In fact, the heavier a baby becomes, the more useful this position becomes because it allows the baby's weight to be fully centered on the babywearer's torso (it's easier on your back.)

Tummy-to-tummy with a straddle carry:  strictly for toddlers and expereinced babywearers.
Tummy-to-tummy with babies with some neck control all the way through toddlerhod.

The kangaroo/buddha carry is a favourite of parents of babies at the peak of squirminess (think 9-mo-old crawlers) because a baby facing outwards is a baby enthralled with the world.  Keep a hand on your baby.....some babies when put in this position are very inclined to dive forwards.
Kangaroo Carry/ Buddha:
For babies 3mo. thru 10mo
(or until the baby is too large/squirmy to sit safely in this position).
For toddlers, I highly recommend tummy-to-tummy with the baby straddling the sling (aim for maximum baby butt and back coverage with the sling fabric but leave one leg out.):
Ring Sling Front Carries:  Tummy-to-tummy, Straddle, Kangaroo & Buddha holds for babies.
 

I personally feel that the kangaroo carry is great for when in a pinch, but out of all the positions you can use, it's certainly not my favourite.  From a babywearer's point of view, it takes a lot of work to keep your baby in place while in this position, especially if the baby is at all squirmy.  The larger the and stronger the baby, the more work it takes to keep the position safe.
However, this position is very easy to "pop" a baby in and out; very handy indeed.
1.  Baby faces out.  Fold your baby's legs up towards his/her tummy and open the sling pocket.
2.  Gently drop the baby's bottom into the pocket and make sure that fabric is smooth against your torso, under tension in front of the baby, and cupping the baby's body.
3.  Baby's legs can be either "froggied" in a squat or, if the infant is very flexible, folded up with toes towards chin.
Straddle carry side view.
Copyright 2007, Sweet Things Baby Slings, LLC.