How to connect/call to the PSTN network using Arduino?
As already written in the comments, you may use any RS232 modem you can find. They use the so-called AT commands, which is a very common way to exchange commands with this kind of peripheral. You can check on wikipedia or on google to get more information on it.

The main problem is that this kind of modems are a bit hard to find (or at least, they are a bit harder to find and a bit too expensive for my liking). That's why, for a project of mine, I wanted to switch to a cheaper alternative. Looking on the internet, a lot of people stated that it was much better to have an already approved instrument rather than designing your own. For this reason, I bought a mini-phone like this one:



You just have to open it, wire the keys (or rather, the rows and columns of the keypad) to the arduino and let it do the magic.

This solution is cheaper (I spent 4€ for this, but if you have an old phone it becomes free) than getting a RS232 modem, but needs more work on your side.