Here is a very basic set of instructions on how to use Premiere to convert your animated frames into a Quicktime movie. This is an attempt to do it in as few steps as possible.
You should render the frames of your animation such that each frame is in its own image file. You must use a file format that Premiere knows, but it knows about a lot of different image types. It does not know about the Maya image file format (iff). If you made these, you can convert them to TARGA using the Maya image viewer. Use the "Save As Animation" menu option, and select Targa as the file type. (Targa is a good choice for the image type - it is losslessly compressed).
Your files should be named xxxNNN.ext (where xxx is a name, N is the frame number, and ext is the appropriate extention for your file types). For example, mine are "ball000.tga", "ball001.tga", ... It is important that all the numbers have the same number of digits. The maya image converter doesn't do this for you. Converting the file names is a drag, I have no good answer for it.
When you start Premiere, you will be given a "new project settings" dialog. You might try "load" which will give you some presets. The "multi-media quicktime" settings are a good default. (if your original images are 320x240 - if not, Premiere will scale them for you). It also picks a reasonable compressor.
Under the "file" menu, pick "Import->File". Pick the first image of the sequence, and check the "import sequence" box at the bottom. If everything works right, your project window should have a new entry with the name of your first frame, a type of "animation", and a duration that is how long your animation would be at 30 frames per second. If you double click on it, you'll get a clip player window so you can watch your animation.
I recommend saving your project at this point.
I have noticed that sometimes, the importer does the wrong thing if I give it the first frame of a sequence. In this case, you'll see the clip imported as a single image. Usually picking the second image of the sequence works.
If your animation is not rendered at 30fps, select it (single click the line in the project window), and then pick "Interpret Footage" in the File menu.
The Timeline is complicated, but for the basic procedure of making a "movie" of just your clip: Drag the clip into the timeline, so that the beginning of your clip is at the beginning of the timeline. You'll want to drag your clip to the row called "Video1A"
From the file menu, pick Export->Movie. Make sure the file name has a .mov extension (if you're doing Quicktime).
Well, maybe. If all went right, you've just converted your image files from Maya into a Quicktime movie. There's a lot more you could do with Premiere.