The pace of the quickstep is just as the name suggests--quick. To stay light on your feet and keep up, place your weight in the balls of your feet. The basic counting rhythm for this dance is slow-quick-quick-slow, in which the slow counts are about twice as long as the quick counts. This dance usually features jazz or swing-style music.
For the lead dancer, step forward on your right foot (slow), step to the side on your left (quick--your feet should now be parallel), bring your right foot to your left to step your feet together (quick), and finally step back out to the side with your left foot again (slow). Step back on your right foot, step to the side on your left (feet parallel), step your right foot together with your left, and step out on your left again.
For the lead's partner, step backwards on your left foot, to the side with your right, bring your left foot in to meet with the right, and step out with your right. Then step forward with your left foot, to the side on your right, bring the left foot into the right, and step out with the right.
To cover greater distances on the dance floor--and to add some flare to the first basic step--the lead will initiate the step out.
For the lead, the footwork for this move is the same as in the previous step, but rather than moving the right leg backwards after doing a forward basic, it is moved out to the forward left, on the outside of the partner. Continue by stepping forward with your left (feet parallel), right foot to your left foot (feet together), out on your left. (These last steps are a basic move again. Once you are comfortable with the quick step, the progressive chasse step out will lead into other moves after the initial right foot steps forward outside of the partner.)
For the partner, the footwork does not change, but you will have to adjust your body angle and direction of steps to be in sequence with your partner.
The final basic step in quickstep is slightly more complicated than the previous moves.
For the lead, with your weight on your left foot, step out to forward left with your right foot, as in the step out. Your right foot will be diagonal; step your left foot forward so it is also on a diagonal but in front of and out from your right foot. Step your right foot directly behind your left so your ankles are "locked." Shift your weight to your right foot, and step out with your left. Step out forward left with your right foot, step to the side with the left (feet parallel), step your right foot into your left and your feet are together, and finish by stepping your left foot out to the side. You have completed the basic patterns for the quickstep.
For the partner, start with your weight on your right foot, step backwards with your left on a diagonal so your left heel is pointed towards the right. Step backwards with your right foot so it is on the same diagonal as the left foot, just placed further back. Cross your left foot in front of your right, and "lock" your ankles. Shift weight to the left foot, and step your right foot out to the right side. Step your left foot back (feet parallel), step your left foot into the right, and finish by stepping your right foot out to the side.