Could someone please explain to me how the auto focus works whilst videoing. Does it continuously auto focus or should i half press the shutter?
Nikon D3300 supports AF-S and AF-F modes for video recording. AF-F helps you to keep focus without touching the shutter release button. This page says that you never touch the shutter release button in AF-F mode. Just turn live view on, switch your focusing mode to AF-F, and wait until the camera focuses by itself (unlike what you do with a normal autofocus system while taking stills). Once the camera has focused, you can press the record button. Focus will be updated automatically.
I usually use manual focus, and tried AF-F to answer your question. It works well, except under low-light conditions (that's the reason for some issues, I think).