attempting to render my first animation

Ok, so it is rendering now, the little bar at the top, is moving.

how long does this process take (I’m on a laptop), does it go frame by frame.

Frames are rendered one at a time. The frame render needs to be completed before the next frame is rendered. It will take however long is needed. This no-one can tell you as it is all dependant on your scene and your settings.
Look at the top of the render window to show the time taken to render the frame.
For a total estimation on render time you can use http://wiki.blender.org/index.php/Extensions:2.6/Py/Scripts/Render/Render_Time_Estimation

VERY IMPORTANT - Set your render output format to an image format such as .png, NOT a movie format. If you chose a movie format you may get to the last frame and blender crashes. You have wasted all the hours that took to render. Using an image sequence you can stop/start at any point with the most losing the current frame being rendered.