This is really basic stuff. Think Layers.... You'll need to create the smoke. For that you can either shoot it against a black background, use a particle system, a fractal noise system, or buy some stock footage. You then just put the smoke layer above your footage and adjust the position, blend mode and color balance to match. If the camera is moving then you'll need to track the shot and apply tracking information to the other layer. Without a more detailed description of your shot and the resources you have I can't give you much more help that that.
As Rick says, this stuff is pretty basic in theory, although, each shot produces its own complexities.
In order to work in AE, you must have a good foundation in how it works. I highly recommend that you start here. It will save you much frustration in the future.
The "VideoCopilot Frosty Breath" tutorial by Andrew Kramer might be of some help but it uses the Trapcode Particular plug-in.
If you don't have Particular I would highly recommend the following method using Turbulent Displace, which is a built-in effect in AE. I personally think it creates excellent fog/smoke layers which you can animate, keyframe and control manually:
a.) Create a white solid.
b.) Mask it into a shape that more or less represents the way you want your fog or smoke to look.
c.) Adjust the mask feather to about 500 pixels. You can change it or animate it later once it's in your scene.
d.) Add the Turbulent Displace effect to the white solid layer.
e.) Change the complexity to 6.0 and if you want the displacement of the fog to change over time I would suggest animating the offset and possibly the evolution.
f.) Then if you want the fog blowing across the screen I would suggest animating the position and possibly also the mask path.
g.) If the fog/smoke is too opaque you can adjust the opacity.