You need to make sure that the file you are rendering as contains transparency. That means in your output module, you need to set it to render RBG+A and you need to choose a format and codec that support alpha (such as Quicktime with the PNG codec or certain flavours of ProRes).
When you get time, I highly recommend going through these resources to get a foundation on this sort of basic functionality of AE. Actually understanding how to use After Effects will actually save you a lot of time in the long run.
I apprecaite the quick response and I will look into the resources you recommended. However, I don't think my problem is exporting at this time. In order for me to find an output module of RBG+A, I needed to go to cutsom. It wasn't there until I toggled the transparency grid (unless I botched that up) and then used a custom output with RBG+A. It didn't work.
You don't need anything custom, you need to use a codec that supports Alpha Channels. In Quicktime, there are three: Animation, PNG and ProRes 4444. Of the three, I'd go with the ProRes.
When you render out your movie to preserve transparency, make sure you're set up for RGB+Alpha, Millions (or Trillions) of Colors +, and Straight, i.e. not premultiplied.
If you don't have a transparent background behind the smoke in After Effects, you will need to find a way to key out the smoke. You can either do a luma key or you can use the free Unmult plugin from Red Giant.
Try just setting the smoke layer to the Screen or Add blend mode.
Remember that white plus white is going to be white so the areas of your background that have white clouds will not show any smoke even if you had a perfect key because white + white is white. IMHO that cloud background is a terrible choice for a smoke to text effect.
Dave mentioned codecs that support alphas. He missed a few. PND Quick Time and Jpeg 2000 also support alpha channels. So do image sequences using png, tiff, tga or psd files. All of which will read in PPro or FCP, but if you have no alpha in your AE comp then you need to make one with the techniques suggested or just use a screen or add blend mode.