from a pocket cam made by Flip to a Panasonic PVGS320 to a Canon HF S100 to a Sony HDR-FX1 to a Panasonic AG-HVX200... and a lot of others between and above basically behave the same way when in "auto" mode. Even a little Canon PowerShot SD1000 camera is essentially the same...

Insert the video or image storage media,
press the power button - and be sure the camera or camcorder is in video record mode,
point the camcorder at the subject to be recorded,
press record.
When done, press record again.

To recharge the battery, plug the AC adapter into the wall and the camcorder.

When the storage media is full, remove it and put in a blank. The same can be said for point-and-shoot digital still cameras that happen to capture video as a convenience feature.

As the cameras and camcorders increase in price, the available options (including manual capabilities) increase, but you don't need to use them.

Do you have a budget? We can start there... More or less than $500? What sort of video quality are you expecting? Might they be more comfortable with a DSC that can also capture low quality video instead?