Making a Mac Mini mid-2007 able to display 2560x1440 in 2D work I have a Mac Mini mid-2007 (MB139xx/A) that can only output 1920x1080 (as far as I've understood).
I have a Dell U2713HM screen, and I'd like to make that Mac beeing able to work on that screen at full res. Not for gaming or such 3D contents, just for simple 2D display (Finder, text writing, Web surfing, etc...).

Do you know some trick that can help me to achieve this goal ? I've read many things about connecting an external graphic card via USB, PCIe, Thunderbolt, etc... but I'm not a Mac hardware expert and I don't see anything that could work with no doubt on my Mac.

Can you help ?
With a Mac Mini that old, you are out of luck if you want anything better than the built-in HDMI.  However, there are USB-to-DVI converters, also known as external graphics cards, that will work fine to connect a second display.  I have had good results with this one.  Two 1920x1080 monitors are a lot better than one!

Newer Minis (the 2008 Core 2 Duo model with GeForce graphics, and later) have two video ports, one of which is a DisplayPort connector which with the right adapters can run a 30" monitor at 2560x1600.