Learn the basics of the waltz by familiarizing yourself with the basic steps used in waltzing such as the box step and the waltz forward progressive step.
Begin with the box step. Start with your left foot on the ground, and placing your right foot on the ground about a shoulder width away. Move your left foot up next to your right foot in this position, and all motions should happen in the three-quarter step time. Finish the box step by moving your right foot back a step and your left foot shoulder width apart to the left in the same line as your right foot. On the last count of 3, move your right foot so that your feet are together.
Try the waltz forward progressive step. Instead of stepping back after the first beat of 3 as with a box step, do the first half of the box step and follow it up by moving your right foot up a step and your left foot on the count of 2 a shoulder width apart to the left. Finish this step off by moving your right foot next to your left foot and repeat all 6 steps to continue the waltz forward progressive step.
Practice these steps until you feel comfortable that you can do them without worry of slipping up. And learn other basic steps by consulting a manual on waltzing for these steps as there are many variations and they require lots of practice. Use the Internet for visual references on foot location to better illustrate each movement more specifically.
Find a partner. The only way to do a ballroom-style waltz is to find a willing and capable partner who you feel comfortable dancing with. Practice with them to get the steps down.
Learn the posturing. If you are leading, place your right hand at the small of your partner's back, and hold her left hand at about shoulder level. Keep your back straight. If you are being led, place your left hand on your partner's shoulder, and hold his hand with your right.
Coordinate the basic steps and integrate more challenging steps into your routine. The key to ballroom-style dancing, besides knowing the basic steps, is knowing how to seamlessly mix these basic steps with a more complicated regimen of moves.
Practice, practice, practice. In any dance style there is a substantial amount of time put into learning not only the basics, but the appropriate posturing and the timing with a partner will make your dancing flawless. If you are in a competition, you will need to choreograph your movements ahead of time and be comfortable enough with each other to move gracefully around the room.