My Ballroom dance teacher told me the best place to find a partner was in the computer labs. Geeks can dance all they need is a manual. Lets start from the beginning.

THE STANCE: Imagine the lead is wearing a buttoned shirt. The follower should align him/herself so that the leader's buttons are down the follower's right side. Both bodies should remain parallel at all times and the same distance apart. The leader extends his/her left hand as if shaking but to the side. The follow extends his/her right hand out and clasps the leader's hand from the top. These arms should be positioned about the height of the follower's chest.
A good lead needs to let his/her follow know where to go. I know you want to put your hands on each other's ass, but this makes for a terrible lead. And remember a good dance can lead to a good shag. Both partners should put their remaining hand on the other's shoulder blade. Elbows parallel to the floor. Having your hands in this less provocative position helps direct the follow if he/she is leaning a bit onto it. This is the basic closed position for most ballroom dances.

THE WALTZ Now the waltz is a particularily pretentious looking dance. Both partners should always be dancing on the tips of their toes and looking off onto the imaginary bleachers with a apathetic face. These techniques will come with time. Stare at your feet if you must, but work on looking up a bit. Evening wear and heels are not necessary, but slippery soled shoes on both partners will make life a lot easier. I would never recommend girly shoes under any circumstances.
Let us not forget that dance is an art of taking up space. The steps described in How to Waltz is the basic box pattern. Great for crowded club floors, but not spectacular when you have plenty of space. As zot-fot-piq said, "It's all about fun." Who cares if there are other dancers on the floor? Plow em down! 15 points for elderly couples. Set goals. Try to make it across the floor without a fumble.

To break free from the box: Practice the steps in How to Waltz. Now forget half of it. I'm not good w/ ASCII art or diagrams in general but here goes:

THE FOLLOW: Follow is generally a woman. I personally lead from follow position because I know when I want to spin, but technically you are supposed to do what your title dictates. Wait for your lead to direct you. When he/she enters your space move back to avoid a foot crushin. The follower always starts with his/her right foot.
STEP ONE: On the first beat, simultaneously bend your left knee slightly and move your right foot backward one step shifting your weight to your right. The slight bending of the knee creates a slight dip. The waltz is meant to glide dip and sway. Each time you move a foot, the standing foot will lean off the toes. On the recover, the foot in motion should end up back on its' toes creating an upsweep.
STEP 2: This is a tricky one. It will look awkward if you robotically push your left foot back diagonally (/ ), but you want to end up with your feet aligned and apart. (0 0) As you are leaning your weight onto your right foot (from step 1), sweep your left foot back toward the right foot making a soft inward curve to your left. On the second beat, set your left foot down approximately two feet away from your right foot. At this point you should be standing with your feet aligned again, and your legs apart like any lady/gentleman in an evening gown yearns to be.
STEP 3: The anticlimactic legs together step.
Your weight should now be on your left foot. The beauty of dance is we will never try to make you place the weight on the same foot over and over unless you are trying the boot scooting boogie. (Which I don't recommend) All you have to do in this step is take your right foot and move it closer to your left foot on the third beat. Again this should be in a gliding upsweep motion. Unless your upper body is a board you will find you shoulders sway left as your feet sway right and vice versa. This is good, but don't over emphasize it.
To break free from the box:
STEP 4: Instead of moving your left leg forward in the box pattern, move it backwards one step. That's right kids, we are moving backward instead of in circles. (On a side note the lead can dance backwards as well. In this case you have to steer to avoid collisions) Don't forget to bend your right knee slightly as this is happening.
STEP 5: Sweep your right foot towards your left with an inward arc then out to the right side. STEP 6: Move your left foot together toward your right foot.
Repeat steps 1 through 6 to move in a relatively straight line
Back, Left. Together; Back, Right, Together; Back, Left Together; Back, Right, Together
One, Two, Three; One, Two, Three; Back, Side, Together

THE LEAD: You are the leader. You decide when to start, where to go, and how large your steps are. I personally recommend small steps, holding your partner firmly, and counting out the beat. The waltz is in ¾ time only. Do not attempt to waltz if there isn't 3 beats per measure. Find the beat. BOOM, tap tap, BOOM, tap tap. Count aloud. One, Two, Three. One, Two, Three. Then carpe scrotum.

STEP ONE: The lead always starts on the left foot. On one, bend your right knee slightly and move your left foot forward one step. There you've done it. You are in motion. Read the follower's instructions for the more advanced techniques of dip, sway and sweep.
STEP TWO: As you are switching your weight onto your right foot, sweep your left foot toward your right foot with an inward arc. Then step down to the right side on the second beat. Your feet should be a step apart and facing the same way. (0 0)
STEP THREE: Slide your left foot toward the right one shifting your weight with a slight sway in the upper body. On the third beat; shift your weight to your left foot, which should now be close to the right. (0 > 0 ) to (0 0)
STEP FOUR: Breaking free from the box.
Bend your left knee slightly, and take one step forward with your right foot.
STEP FIVE: As you are shifting your weight to the right foot, sweep your left foot forward and inward arch it to the left. (0 0) Legs apart on the third beat. Yay!
STEP SIX: Slide your right foot to the left. Legs together (0 0)

REPEAT steps one through six until you run into a wall.
The catch is you don't really want to run into a wall now do you? Ballroom dancing is generally done in an oval shaped room. Steering is useful, but not nearly as fancy as a few WALTZ QUARTER TURNS. Four quater turns will spin the couple 360 degrees in 4 measures of music. This move is very eloquent and a much more dazzling maneuver than the standard box if the floor space is limited.
To avoid a wall or another couple a few quarter turns will switch partners from moving backward to forward and forward to backward. Breathe. Don't Panic. It's not that hard.

When you want/need to turn: Back, Side, Together
THE FOLLOW: If your lead wants to run you into the wall that is his/her prerogative. However, should he/she decide a turn is in order, you should feel the lead turn you slightly with his/her upper body as the turn is initiated. The lead and the follow have the same Forward side together, back side together pattern only with mirrored feet. Thus, I shall only explain this once for the follow. Lead starts back side together with the left foot.
STEP ONE: Bend your left knee slightly and move your right foot back just like the original step 1.
STEP TWO: This is where all that sweeping practice comes in handy. This time on the sweep you want to end up with your left foot perpendicular to your right instead of aligned with it. The sweep is not toward the other foot. It is more of an outward arch. (_| Your feet should end up pointing at a 90-degree angle.
STEP THREE: Another outward arch to bring your right foot back into alignment with your left foot.Holy crap you are facing a different direction.
That was a waltz quater turn and this is where it gets fun.

Forward, Side, Together
STEP FOUR: You get to take the lead from follow position. Aww yeah, moving forward. Take your left foot and swing it forward to the left in that same outward arch position. Land it one step forward at a 90-degree angle to your right foot.
STEP FIVE: Now swing that right foot in a forward arch so it is parallel with the left foot but spread apart.
STEP SIX: Step your left foot back closer to the right.

At this point you have made a 180-degree turn. (Two waltz quater turns) The severity of the angle is for the lead to decide. If you are dancing in a large ballroom and you are using these turns to steer around the corners you may have to do step one through three. Move forward a few more steps then use steps five though six to round the second corner. This is difficult for beginners because the lead would then be moving backwards and this node is getting too long to explain it. If you are dancing in limited space you may wish to use the entire waltz turn as a variation on the basic box pattern. To do this simply repeat steps one through six again and you have made a 360-degree turn. (Four waltz quater turns) Spin around ad nauseam. Now go wow em at that wedding!