The Fritz!Box is really a very usable device. And I am quite happy that it is pretty common and many people have it. Here I describe which features I especially like and use.
The easiest way to configure it is probably accessing it via your browser, just navigate to either http://192.168.178.1/ or http://fritz.box/. Sometimes I have not set up correctly DNS properly because I have a half-ass configured VPN running on one of my laptops and then I have to use the IP insteda of the domain name.
What’s really handy is the feature to log into your box when you are actually not home, for this you either can use DynDNS where you need to register with a provider, some of which cost money. Or you can use AVM’s own service called MyFRITZ.
Just create a MyFRITZ account, then log into your box when you are home and navigate to: Internet -> MyFRITZ! and click on Add MyFRITZ! account.
Now you have to give your email adress and details on the MyFRITZ account.
From now on your box will send its current IP adress to the MyFRITZ service and thus you can access this box via the domain name you got registered on your MyFRITZ account. You also could register several boxes there, for example if you adminster some for your friends or family.
After this go into System -> FRITZ!Box-Benutzer and click on Add new user. Fill in a name, E-Mail and password and most importantly check the box Zugang auch aus dem Internet erlaubt.
If you type in the adress you got from the MyFRITZ then you will be forwarded to the FritzBox login and you need to log in via the user details you just set not with you MyFRITZ one! Also this user and password is only stored on your device and not on the external service. The external service is just to create a domain name to access your box.
To view your domain name you need to have enabled: Internet -> Freigaben -> FRITZ!Box-Dienste -> Internetzugriff auf die FRITZ!Box über HTTPS aktiviert and then take a lookt at Internetadresse Ihrer FRITZ!Box.
Click on Telefonie -> Telefoniegeräte and then on Neues Gerät einrichten. Choose Telefon (mit und ohne Anrufbeantworter) and then most importantly LAN/WLAN (IP-Telefon) the rest is just which numbers to use and whats the internal number is going to be.
Now install Ekiga click on Edit -> Accounts and use the following example to configure yours:
Name: My FritzBox
Registrar: fritx.box
User: 1
Authentication user: 1
Password: XXX
Timeout: 3600
Registrar can also be the IP of your FritzBox if you have not a correct DNS (like me right now). User and authentication user is the your phones internal number, which can be viewed in the settings.
Now you can make calls from your computer!
You can even log in on your own VPN now and thus phone from anywhere you currently are and access all the computers in your network at home. Go to System -> FRITZ!Box-Benutzer then click on the Edit button to the right for your user. If you have on the following page enabled VPN you can now click on VPN-Einstellungen anzeigen to get the details on how to connect into your own VPN.
AVM also releases nice Videos on YouTube which give good instructions on how to edit those settings and what they are actually about. The relevant ones for this subject are Die FRITZ!Box am IP-basierten Anschluss and VPN mit der FRITZ!Box .
Some other relevant links might be this and this you can learn there how to have a GUI for the FritzBox on Linux or add Thunderbird contacts into yourbox for example.