Hi Dale,
I do exactly the type of work you're talking about.
Essentially there isn't an easy way to create true infinity in 3D animation -- it always involves a certain amount of trickery.
The first step is simply with art direction, i.e. if you can design your shots in such a way that the area of focus is relatively small, avoiding "panoramic" shots, then you will face less challenges with creating the illusion of depth and infinity. Avoid gratuitous camera fly-throughs (this is a battle we have with art directors all the time).
So far as creating infinity -- there are a number of approaches to this depending on circumstances. If you need true 3D objects then object instancing or particle instancing are ways to get a very large number of objects through a renderer. However this approach has its limitations and can be technically difficult to set up and manage for the less experienced.
Another approach may be a series of texture and transparency mapped planes or spheres, overlaid one behind the other to create the illusion of 3D depth and parallax. I have used this approach to create a background for a neuron field in the past. I had a series of ever larger spheres, with the main action occuring inside the smallest sphere. True 3D elements populated the principal area of action, so the background spheres were only ever seen through or past true 3D objects.
The "cheapest" method is simply a post process, done in a program like After Effects. It's possible to get camera animation and nulls out of Maya and into After Effects. A skilled compositor can then take this data and attach 2D or 3D elements or images to them in AE. Your 3D elements are then comped in on top of that to create seamless animation.
HTH!