Create your base movie. If you need to, import it to your computer.

Open After Effects.

Choose New Project.

Drag your movie into the project window.

Drag the movie from the project window to the timeline window.

Move the play head to the point where you want the laser to begin firing.

From the menu, choose Layer/New/Solid. Name the layer Laser 1 (or laser 2, or laser 3).

From the menu, choose Effect/Generate/Ellipse.

Adjust the colors, width, height, thickness, softness, and position of the ellipse to put it in the right starting position.

Click the triangle on the laser layer. Sub-layers will appear. Click the triangle next to transform.

Click the stopwatches next to Position and Opacity. This will turn on keyframes and add them at play head.

Move the play head back one frame. Click the diamond on the far left of the Opacity layer to add a new keyframe.

Set the opacity of the new keyframe to 0. This hides the laser until you want it to appear.

Move the play head forward six or seven frames. Click the diamond on the far left of the Position layer to add a new keyframe.

Drag the ellipse off screen in the direction the blast should fire.

Repeat the above steps for each laser blast.