How do I get emission nodes to create glowing eyes like he does in Cycles, but in Internal?
Don't expect people to watch a whole video to answer your questions, please describe what you want to do with words, add reference images and post what you have done so far.
The glow effect in that tutorial is made using the compositor, not the render engine itself. The compositor works the same way for every rendering engine so the techniques described there should work both for Cycles and Blender Internal.
Just add a Glare node with fog glow and it should work identically.
As for the material itself you can use the Properties Window > Materials > Shading > Emit option or alternatively activate the Shadeless checkbox right beside it.
Adjust the emission intensity as desired.