How did you buy your current FTM and what version is it?
Regardless of the version, if you have the original CD, just put it in your DVD/CD drive and it will install on your new machine. If it is a really old version, you may have problems.
Data files (including FTM's data files) from your old machine under My Documents will transfer to My Documents under your new machine. I presume that can be done over the network - or with an external drive - or a direct pc to pc cable.
When you first open FTM in your new machine, you will need to use File > Open and browse to the file. After that, FTM will remember the last file used and open it automatically.
If you purchased via download, you should have the zip ftm file in your download folder. Find that zip file and transfer to your new machine and click on the file. It should automatically unzip and install. This file will need the updates since that version. I would go to Help > Check for Updates. If you can't find the zip file, I would call FTM and ask what to do.
As I recall, FTM's license is "one license for one machine", meaning, I guess, that they want you to remove FTM from the original machine. But, who will know if you don't?
The one thing you can't do is to be online from two computers with the same ancestry username at the same time. Ancestry.com will catch that and won't let the second computer in.
FTM software is not supposed to be networkable, but I'm no network expert to know exactly what limitations that means.