The simple way when using a PC is to set the camera up as a 'Skype' feed. The user then 'calls' the PC (which is set to 'auto-answer') and gets the video.
However (as usual) things are not so easy with the Pi - the drawback is that Microsoft (owners of Skype) don't want you to do that without running the entire 'client' on the Pi (as well as paying them a fee) - so the Skype 'SDK' based solutions no longer work
The Pi can act as a 'streaming video source' which VLC (running on your PC etc.) can view. The advantage of this is that the Pi does not need to add 'file headers' etc to the video == it just streams it straight from the GPU to the Ethernet port. So all you have to do is connected the two devices via your network eg. using 'netcat' or (via the web) SSH (see here and here for some 'pointers'). The drawback is that you need to run VLC on the 'remote viewer'
The Pi can deliver at least 30mbs via it's Ethernet cable, so you can get full 1080p HD at max. quality, max. data rate (25mbs) across your LAN (you may have to overclock the CPU since the Pi Model B Ethernet is off the USB hub and the USB drivers are 'crap' i.e the data rate is CPU limited).
Whilst it's possible to run this as a 'web viewing' solution, you will be bandwidth limited by your Internet 'upload' speed, which is about 1mbs (from TalkTalk, Sky, O2, AOL and all the 'Supermarket' ISP's). Even though Virgin, BT and Plusnet have upload speeds of 4-5mbs, you still won't get 'high quality full HD' - at best you can expect 'half HD' (720x1280) at 25fps and high compression (or lower frame rates with better quality)
There are two main approaches .. the 'local' solution is to run your Pi as a web server, the 'remote' solution is to have the Pi 'upload' the video stream to a web based server (eg 'dropbox') or to your own web site (and let the web site hosting company stream the video around the world).
The main drawback for all 'remote' solutions is the limited bandwidth made available by all ISP's for web uploads. Most ISP's limit you to 1mbs or less - only Virgin, BT or Plusnet give you 4-5mbs - which effectively limits you to 1 full resolution still photo every N seconds (a 3.5MB (MegaBytes) jpg photo is 28mb (megabits) = so even at 5mbs that's going to take over 5 seconds to upload) or a very highly compressed, low resolution, low frame rate video stream (which you can expect to be 'worse than Skype' since they use very clever algorithms to optimise their video feed)