Hello! Let me answer your questions.
First, should I copy over the technology file and the accompanying folders to my mod folder and then use Cretech on that? Right now it is at the file withing Beyond the Sword.
It doens't really matter where your file actually is. Cretech only loads a copy of the file, and it doesn't even remember the location of that file. After exporting with Cretech, just open your tech file with any text editor (e.g. Notepad), and replace its entire contents with the output generated by Cretech. (Note: backup before you do so.)
Second, what is the best way to figure out the X and Y coordinates of the tech tree grid for a new technology?
The best way is to draw a map (personally I prefer by hand). The X coordinate is measured in entire tech widths -- that is, techs will never overlap each other if they have different X coordinates. The Y coordinate is measured in half tech heigths, so if two techs have the same X coordinate and a difference in Y coordinates of 1 or less, they will overlap. My tip would be to experiment a little with it, using the tech tree generator in Cretech.
Finally, how do I deal with quote, sound and button inputs at the top? Should I just copy in similar technologies?
Those inputs are rather tricky. They refer to tags of objects in other files. You will have to create new objects (with corresponding tags) in those files as well. Those objects also specify exactly which sound file or button image to use. So simply inserting a new tag in Cretech is not enough, you will also have to add that tag to another XML file (something with sound or graphics respectively, right now I can't check it) and specify a path to a sound file/graphics file in those XML files.
If this doesn't make any sense to you you can PM me, and I will try to explain more clearly, possibly with acces to those files to give you some more info about it.
Currently, I am working on a generic Database editing program with XML importing. Once it's finished, any XML file in Civ4 will be editable with it, so adding those sounds and buttons will be a piece of cake.