Is your 20 x 10 matrix single color or multi-color (as in 2 or 3 color LEDs - just means a lot more connections)?
You are basically talking about creating this, but twice as wide.
To turn an LED on, you need the combination of an Xrow being high, and a Y column being low to put voltage across an LED.
To multiplex it you will quickly set up the Ys, turn on X1, then turn off the X1.
Set up the next Ys, turn on X2, turn off X2
Set up the next Ys, turn on X3 turn off X3.
Do this rapidly enough and it will look smooth.
You can make the array however big you want.
The Ys can be driven by a regular shift register as they only see 1 LED being turned on at a time if you drive the Xs correctly.
The Xs however must be able to source 10-20mA for each Y as potentially every Y could be enabled at the same time, unless you multiplex the Ys also.
So you probably want shift registers controlling transistors to let 5V be applied to the X lines.
You could also look into displays like this to cut down on the wiring needed, here's a 2-color matrix 5x7 matrix
You could arrange 6 of these to make a 10 x 21 matrix.http://www.mpja.com/prodinfo.asp?number=16784+OP
Or maybe 2 of these for a 24 x 10http://www.mpja.com/prodinfo.asp?number=18050+OP
Check out the datasheets, browse around. Wouldn't be that difficult to put several of these and some chips to drive it on a PCB, vs 200 3mm or 5mm LEDs.