Welcome to the site! Feel free to stick around and read threads/ask questions, that combined with messing around is the best way to learn.
The first way you could do it is simply by connecting your phone to your computer and mounting it. Once it's connected, unlock your phone, drag down the Notification bar at the top, and tap "USB Connected" followed by Mount. Note that there is a chance you have to install the USB driver from Samsung for it to work.
Another method is to use something like Dropbox. It's my preferred transfer method - you get 2gb free to start with, and can add more by getting referrals. If you don't have one, I suggest using a referral link from this thread so both of you get 250-500mb more. You can send videos by either long-pressing them in the Gallery > Share > Dropbox, or by using the Dropbox app. Still photos and videos are located on your SD card > DCIM > Camera.
I don't think I've ever been able to send a video via MMS, with this phone or even when I had my HTC incredible, your only options unfortunately is to email or use dropbox as someone suggested earlier. Perhaps if you reduce the quality of the video and time and re-record and attempt to send that might work.
I had the same problem, go to the video camera and click the arrow on the left side so that the side bar opens up, then click the very top icon and select the second option, "MMS Limit Size" or something like that. it wont record in the same quality but it allows u too send quite long videos via messaging, hope this helped!