Smoothing a face

I am new to Blender and 3d modeling in general; therefore, if my question is beating a dead horse, please bear with me.

I am working on a 3d model of a vehicle turn signal as a first simple project.

I want the side of the object to be smooth, but curved. Is there a button I can click to do this, or do I have to make a bunch of smaller planes to get the effect.

I tried the shading: smooth, and smooth vertex commands, but neither got the effect I am looking for.

Here’s a picture.

This is what I am trying to make. See how the edges bow out a bit before returning.

Check this out.

Add a subsurf, then select the edge you have selected, and the opposite edge, SHIFT+s select cursor to selected, the press the “period” which sets your pivot center to the 3d marker, then press S to scale. Also watch the video JA12 suggested.

You may like this, also http://getblended.org/2013/03/working-with-subdivision-surfaces-and-topology/

Thank you.