The software you use really depends on the format of the video itself.
If it was an MPEG file, for example, I'd look at using the $20
Womble MPEG-VCR.
If it was an AVI file, it depends.
Understand that an "AVI" file is not a format. That's a container. If all you know is "AVI", then you don't know the format of your video. You'll need to run it through an analysis program like Gspot.
Saying you have an "AVI" is like telling the mechanic you have a "car". It's very generic info.
You don't need a big NLE like Avid, FCP or Premiere just to trim off the ends of video.
VirtualDub would actually trim many formats in an AVI container, as can
AviDemux. Just load the video, mark the in and out points, tell it to do the "stream copy" video output in the options (so it does not needlessly re-encode), and save the new AVI.
If you grabbed an FLV or MP4 off Youtube, it's not really possible to just trim the file, it has to be re-encoded.
Phones are far too wimpy to handle video processing. Even cutting edge phones now can barely handle photo processing. Video is dozens of photos per second.
Good luck.