I have see this tutorial about LED : NerdKits - DIY Marquee LED Array Display
If I understand well, I could do the same with my Arduino board (I just got it... very newby so sorry if the question is stupid), but since the Arduino Board have 13 ports I could have 5 for the rows and 8 (13-5=8) for the columns x 2 with the trick in the tutorial so a total of 5x8x2 = 80 leds... right?
I just want to point out that the digital pins are numbered 0-13, so that's 14 pins. Plus the 6 that are labeled "analog in" can also be used as digital pins 14-19 (or as many as 21 on the Arduino Mini if I understand the docs correctly).
That said, it is sometimes tricky to use pins 0 and 1 both to communicate with the host's serial port and as general purpose pins. But I'd say you definitely have at least 18 pins (#2-#19) to work with.
so a total of 5x8x2 = 80 leds... right?
Yes but you can't drive a whole row with just the output current capability of the pin you will need a driver IC or transistor or FET. Due to the multiplexing the column LEDs can be current sunk by a pin without any external help as only one LED is on at any one time.
Grumpy_Mike you lost me with the Driver IC or transistor. Why does the guy can do it with is board and it would be too much consumming with the Arduino board?
Your matrix is a set of rows and columns.
Keypads are also often arranged in rows and columns. To check which key is pressed, you power the row pin, and you check the column pin, one combination at a time, until you see an intersection that is passing the signal through.
Light matrix parts can be done the same way. Connect just one row to a HIGH signal, connect one column to a LOW signal, and only one LED will shine. To get them all to light up, just do this process for all rows times all columns, really really fast. Almost no extra power consumption, you can do this with the Arduino with no extra parts, but it can be hard to avoid visible flicker since each light can only be on for 1/64th the time for an 8x8 matrix.
Instead, most people try to power one column at a time, and give ALL of the row pins their power at the same time. This cuts the flicker down a lot, since there's only 8 columns to repeat, not 64 lights to shine individually. Unfortunately, that's too much current for the one column pin of the Arduino, if all 8 lights in the row are burning. So you have to arrange for some higher current sourcing and/or draining, using the parts Grumpy_Mike suggested.