All platforms have a palette on the left edge of the screen that contains 8 colors and two brush sizes. selecting a color changes the active drawing color, while selecting one of the brush cursors will change the drawing cursor as well as the size of the brush: 1 pixel square or 3 pixels square.
On the PyPortal, Use the touch screen to control the cursor. A simple stylus works really well for this. Touch on the palette to change the drawing color or brush. Touch anywhere else to place a spot of the current drawing color at the touched location. Moving while touching the screen will leave a trail. Recall that each time a change in touch location is detected, a line is drawn from the previous location to the new one. That means that if you move faster than the update cycle, you'll get a polygon because points are relatively far apart. You can see this in the photo below. If you want a smooth curved line, move slowly.
On a PyBadge, use the D-Pad (the buttons on the left) to move the cursor. Eight directions are supported, corresponding to single and adjacent pairs of buttons. To select a color or brush, move over the desired place on the palette and press/release the A button. To draw, move while holding A pressed.
The PyGamer works much the same, except that you use the joystick instead of the PyBadge's D-Pad. The current cursor control library uses the joystick to simulate a D-Pad, future version may provide more granular control.