So I'm going to take no response as no problem.
Currently the git repository is setup so that after you clone the repository (checkout) you just run DevSetup.bat and it will link your git directory into your Mods\Caveman2Cosmos folder and build the Assert DLL. After that the mod should run fine, and all changes you make in the git repository will be reflected in game. Full FPKs are built automatically on startup the first time you run, and from then on in later runs only a patch FPK is built to reflect changes since the full ones were made (this is normally instant).
If you normally work by copying to and from your Mods folder then I will leave it up to you to decide how you want to work. Certainly you can just run the scripts to build FPKs and DLL and then copy them over like you would normally do, then any art you add in the Mods folder you can copy back into the UnpackedArt folder.
HOWEVER: I would prefer to work out what your requirements are that cause you to want to copy rather than work directly in the working copy and then address those. I think git with its local branching and merging opens up easier and safer ways for you to work that weren't available with SVN. For instance git can easily allow you to keep and commit into multiple different local versions of the mod, including stuff that is never intended for other people to use.
If you need to merge other data in we can do that in the working copy and exclude it from being detected by git quite easily (or put it into its own branch just for you). if you are worried about accidentally committing changes you didn't intend then you should re-evaluate if that worry is still appropriate after trying git for a while. If you merge changes within the same files locally when you update, then git can make that a lot easiest using local branches. It could save you a lot of time doing updates and you can keep your local changes safe by committing them (at least locally, but why not into the repository as well?).