Training to walk faster will initially feel uncomfortable until your body gets used to working at an increased level of intensity. The following are some suggestions of how you can adapt your existing level of exercise in order to develop the ability to walk faster.
Treadmill - reduce either the distance you would normally cover or the time you'd spend on the machine, but increase the speed of the treadmill so that you can maintain the increased pace for the entire distance or time. When this begins to feel easier, gradually increase the distance or the time at this faster pace. You might then consider adding additional loads such as inclining the treadmill, or wearing or carrying weights.
Step machine - using less resistance than normal, increase the rate of steps for the duration of your session. As this becomes easier, increase the length of time at this faster rate.
Outdoors based training
Time trial - choose a short walking circuit (i.e. begins and ends in the same place). Keep it fairly short, perhaps not much more than one or two kilometres. Time how long it takes to complete one circuit at your normal pace. Then attempt to complete another circuit in a faster time. Ideally it should be possible to complete a number of circuits in each session. Use this as a measure of your progress.
Circuits - using the same circuit as above, time how long it takes for one circuit at a slightly faster pace than normal. Attempt to maintain this pace for each subsequent circuit. Once this becomes easy, increase the pace of the initial circuit.
Jogging or running - is an excellent exercise to help condition your body and get your the legs moving faster. As it's more intensive than walking, it can be a good alternative if your training time is limited.