Australian piano teacher, Tim Buckland, has the best method I've seen for teaching pedaling technique. He suggests you play chords on the white keys, starting on C Major, and going up an octave. Say "Up" as you depress the notes to remind yourself that this is when you'd raise the sustain pedal if it were already down. You say "down" immediately after as you lower the pedal.
I'm linking to his article on the subject here as well as slightly modifying his instructions. You'll notice on his chart that Buckland has you hold each chord for a count of 3 beats. I'm suggesting you count: Up, Down, 3. At the count of Up, play the chord. Depress the pedal on the count of Down. Then as you count 3, lift your hand and position yourself over the next chord. Play the next chord (D Major or, if you only want to play white notes, D minor) to the count of Up. Raise the pedal as you play the chord. Depress it when you count Down. Move your hand to the next chord on the count of 3.
The point of doing this is to get used to moving your hand right after you've captured the sound of the one chord. You'll find this invaluable for learning pieces that require you to move around the keyboard - sometimes fairly quickly.
Buckland also suggests you play a scale with just finger, using the pedal to achieve a smooth, legato line. In this case, you'd pedal every note. I would play the scale the way you normally do first, listening carefully to the sound. Then play it with your index finger, noticing the disjointed effect that comes from playing with just one finger. Next use the pedal, trying to achieve the same legato line that you did using all your fingers. Make sure there's no overlapping of sound from one note to the next.
Click here for Buckland's original instructions and some other variations on his method: Tim Buckland's Method for Learning Pedaling Technique