You want the pictures squished, like on the TV networks when they squish the credits on the right side and promos on the left? That would be a pan/crop issue.
If you want them to be normal size, but overlap, it's a little tricker (well, not much).

Step 1)
make a picture in photoshop (or whatever) the approperiate res for your project. I work in square pixel, so mine would be 640x480 for full screen. Make 1/2 of it black, 1/2 of it white (top/bottom or left/right doesn't matter. It depends on weather you want to do a top/bottom split screen or left/right).

Step 2)
import your video clips and your picture into vegas. Put your video sources on layers (doesn't matter in which order, you will see later why). Then put your picture on the layer directly above the highest video layer you want to use for split screen. Don't forget to make it the length of your split screen!

Step 3)
In vegas, click the "make compositing child" arrow button (on the left of the layer name) for the layer of video directly under your picture. Now your top video layer and the picture should be connected. Infact, the default settings should already make the split screen! If you found out the wrong video is on the wrong side just click the "Mask FX" button between the two layers (on the left, right above the arrow you clicked) and check the "invert" box.

Poof! Instand split screen! :) Fun, eh?