Remove the HD from the old computer and put it in an external enclosure. Then connect to the new computer with a USB. This will transfer files but not programs.
You can also use a USB-to-USB bridging cable between computers.
Use EaseUS PCTrans with a bridging cable to transfer files and programs.
You should be able to do this through your local network - the connection goes through your router not the internet. If both computers are logged into the same microsoft account it should be easy, a bit more complicated if they are not. I used to do this but because I rarely have two devices running at once I reverted to using a usb thumb drive which has become habit - the added advantage is that if anything goes wrong (or I do something stupid) the thumb drive serves as a back-up. Plus you can put the files on the thumb drive and copy it to the second machine later or whenever you choose.
Be careful about using a USB to USB cable - usb also deals with some power and isn't intended for this, (it was always a big no no in the past though that might have changed a bit with the newest standards) unless as said previously it's a specific bridging cable intended for the job.