Loading your videos from your recording device
Each recording device and computer may have its own method for loading videos. Here's an overview, easiest first:
The easy way — send straight to Eye Precision
If you're recording with the EP Recorder app and have paired it with the computer running Eye Precision, you usually don't need any of the methods below. When recording stops, tap Send to paired computer on the phone — the video transfers over Wi-Fi straight into Eye Precision and opens automatically, filed under the subject ID.
The phone and computer need to be on the same Wi-Fi network, and Eye Precision must be open on the computer. If the button is greyed out, open Eye Precision and it will enable within a second or two. This works the same from an iPhone or Android phone, to a Mac or Windows computer.
The methods below are still useful if you haven't paired a computer, if you're loading an older video, or if you need to move a file some other way.
Apple iPhone to Mac
The easiest solution here is to use AirDrop. Make sure that AirDrop is turned on on your Mac (go to your System Settings)
Open the video on your iPhone and press the share button 
Choose your Mac in the AirDrop list
The video will be saved on your Mac, by default in the Downloads folder
Android to Mac
My favourite option for this so far is MacDroid, a program that runs on your app and allows you to access you Android phone. It takes a little setup, but their website walks you through it, and the free version does everything that's necessary for our purposes
Apparently a USB cable should work but I've found it unreliable
Uploading videos to a secure cloud and downloading them onto the computer will work
There are other apps such as AirDroid that I haven't tried myself
iPhone to Windows
I use Link to Windows, which connects an iPhone to Windows and uses Bluetooth for transferring files. Its not especially fast for larger files, but seems reliable
Android to Windows
I have no experience with this, but it should be easy with a cable, bluetooth or built-in sharing options
In all cases
If your phone is paired with the computer and Eye Precision is open, Send to paired computer is the quickest route and skips file transfer entirely. Otherwise, uploading videos to a secure cloud and downloading them onto the computer will work, as will email or transfer services such as WeTransfer