Acces Documents from Internet

If all you are going to be doing is storing and accessing files from a few machines then it may be easier to just use ubuntu one

https://one.ubuntu.com/
you could file sync and share files and folders.

If he absolutely wants a server then Ubuntu has a server edition
http://www.ubuntu.com/download/server/download

there is the Samba FIle server to share files
https://help.ubuntu.com/11.04/serverguide/C/samba-fileserver.html

Samba can also be setup on Ubuntu Desktop without much trouble

Just to be clear, the ubuntu versions shipped as "server" and "desktop" contain the same ubuntu - but the default configuration is different. You can share files from a desktop, and use your desktop as a server -- there is no restriction there.

If you need to configure clients to swap files around on the local network, there are several options. SSH (which includes SFTP) is probably the most secure, if (and only if) you use "keys" and forbid blank passwords on keys. However it does not integrate as well into windows' users workflows, as windows does not natively support SFTP - you need to use tools like winSCP or similar. All traffic between the user and the remote host is encrypted, so it is also safe to use this on open networks, as long as you have authenticated once on a secure network (so you can identify the remote host correctly next time).

https://help.ubuntu.com/community/SSH

With regards to remote login, it strongly depends on the type of connection that he has purchased from his ISP. If he has a dynamic IP address, he cannot guarantee that his computer will not change address. All he will need to do is enter in something like "ssh://bob@123.234.12.1/" into his connection program.

Dynamic IP is typically the default for an ISP, however most ISPs will give you a static IP for a small fee (or sometimes for free). It is possible to configure a dynamic hostname for users, using services like DynDNS, which will give you a subdomain (for free), that you can configure your machine to connect with, for example

ssh://<email address hidden>

Certainly I would not recommend exposing samba shares to the internet, for security reasons, but SSH with keys is fine (you can use tools like denyhosts to lock it down further, but this is advanced). The second option is to use a VPN type solution, but this is also quite advanced.
https://wiki.ubuntu.com/VPN

The above solutions for internet side access are a little tricky to set up, if you have not done such before. To compound the problem, you also need to ensure that if you are using a NAT router (most off-the-shelf consumer routers are configured this way), you need to explicitly add rules for redirecting incoming traffic)