How do I administer /var/www?

That is a protected folder. You need to be root in order to modify this directory.

You can also make gab the owner of this directory by doing

sudo chown -R gab /var/www

sudo will execute the chown -R gab /var/www command as a root (administrator) and prompt you for your password used when setting up the system (most likely the same password as gab).

Once you do this, you can also do

sudo chown -R 755 /var/www

to give write permissions.

#   Permission
7   full
6   read and write
5   read and execute
4   read only
3   write and execute
2   write only
1   execute only
0   none


Reference   Class   Description
u   user    the owner of the file
g   group   users who are members of the file's group
o   others  users who are not the owner of the file or members of the group

The 755 means that the user will have full access, group will have read and execute access and others will have read and execute access.

I was going to suggest you become a member of the www-data (or equivalent) group, but since the directory and the index.html file are both owned by root, you may indeed be expected to do so (as kobaltz suggested)—if you want to avoid Virtual Hosts.
If you go the way of Virtual Hosts, the /var/www directory is merely a placeholder that allows you to verify that Apache is running.

I know it's a bit of a read, but did you have a look at this documentation page or this wiki page?