Changing the ownership to a designated user will not change the users default home directory specified in passwd file. Anyhow, You may achieve this in different ways. But to make it simpler do this by opening up a terminal;
Firstly make a back-up of your /etc/passwd file doing below;
sudo cp /etc/passwd /etc/passwd.back
Once done, edit the file (either with vi or nano), I prefer nano which is pretty easy;
sudo EDITOR=nano vipw /etc/passwd
Locate the created user. A line should reflect as below assuming the user is andrew;
andrew:x:1001:1001:andrew:/home/andrew:/bin/sh
Replace /home/andrew with /var/www/sitename.com & save the file by hitting CTRL+O then enter to save & then CTRL+X to exit. This will direct the user to specified directory. Login as the user and see whether it points to **/var/www/sitename.com by also checking for any permission issues. If permission issue persists, then add the user to the www-data group by doing below;
sudo adduser andrew www-data
EDIT: regarding the comment, I just had a quick search and found some more detail. Well, you may edit vsftpd.conf file located in /etc/ directory
sudo nano /etc/vsftpd.conf
un-comment (remove only the # if its there at the beginning) the following line;
chroot_local_user=YES
Note: Just to be safe, make a back-up of the configuration file before you make any changes to it.
sudo cp /etc/vsftpd.conf /etc/vsftpd.conf.back
Source: vsftpd.conf on Ubuntu
Hope it helps!
(Not sure why a question from 2014 pops up again on the homepage, but anyway :D )
It's probably not a good idea to mess with the overall permissions of the rest of the file system, like it has been suggested in the other answer. A better way would be to use a feature called "chroot".
"chroot", short for "change root", just does that: It changes the root of the directory tree the (FTP) user can acccess to what the admin wants it to be. Sometimes the same feature is referred to as "jailing" the user in their home directory.
Most FTP servers support chroot (with the exception of some very small, bare-bone ones). I'm not really familiar with vsftpd, but according to this how-to on Cybercity you need to set the config directive chroot_local_user to 1.
Best Answer
What you're asking for is essentially known as a jail, wherein a user is confined to a certain subset of the system (like say, the home folder). Fortunately, users on Linux already have a home folder setup, so you can just use this jail.
Now, setting up a jail is a complicated matter, and is out of the scope of this question.
Now, assuming you have a working jail, you can just bind the proper folder to the user home:
Although, this honestly is not a good option. If you're just hosting a user, allow them to connect over FTP and just jail them to their "home" (the folder they have admin to). There is no need for them to have a shell on your server.
The question you linked has a very good concept of how to jail users, but it only works with FTP and derivatives, not with raw SSH itself. And, as I mentioned before, running raw SSH is a really bad idea.
Finally, it seems as though you're acting as a web host. Why not just use a control panel like Froxlor? It takes care of most of the heavy lifting for you, and allows you to set quotas and other things that may be of interest. Plus it manages FTP jails and similar automatically for you, allowing you to bypass the headache that is jailing.