An "alpha" is a grayscale image (texture), loaded in the alpha channel of a C4D material. When such material is used on an object, the part of object, covered with black parts of the alpha texture will become transparent. Using that technique you can make a blade of grass or any other shape, even complex one, out of a single polygon.
Use of alpha channels is basic stuff and I doubt you'll find tutorials on the web - as it is well explained in the Cinema 4D Manual/Help.
I don't intend to copy the basic stuff from the Manual/Help here - I suggest you take a look there, into the explanation of using the Alpha channel when creating materials. There's also a short tutorial there, about how to create a complex tree out of a single polygon using the alpha channel technique. If you read it and try it, I bet you'll have no problems with creating a blade of grass or even a feather using the same technique.
In Cinema 4 10 Help System it is located here:
Manual - Reference - Material Manager - Material Editor - Alpha
In Cinema 4 9 pdf Manual, it is located in chapter 18, page 772.
When you get into a problem that you can not resolve by using the manual/help in Cinema 4D, I'll be glad to help you here on the forum.
As for the pricing - I agree. My personal opinion is that all the software companies should at least give away older versions at affordable prices or even for free, strictly for non-commercial use - for young people, who are not students (enrolled in a colege or university) but are interested to learn the program. Why they don't do it, that's out of my scope...
There are other options, though: check the Maxon online shop (http://shop.maxon.net) - you'll find the basic R10 package for only 815 EUR - and you can then buy only the additional modules you need.
There's also a free 3D program, called Blender. It is a very good program (considering the price).
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Is there anything you remember when you were first starting in C4d that you practiced modeling?
My first project in C4D involved creating a Pepsi can. It was in version 2 of the program, on an Amiga platform, about a decade ago. Before using Cinema 4D I used Imagine and Real 3D, and before that Sculpt Animate 4D. Unfortunately back then there was no Internet and forums like this to ask others when stuck or to get tutorials. We learned mostly from printed CG magazines, manuals and by trial and error 