how to extrude an edge that stays connected with the face? I'm trying to extrude the face to create another wall. It works out well but the vertex and edge are not connected to the floor even though it's level. Anyone know how to extrude so it stays connected with the face? If it's even possible.

Thx

Screenshots:
I assume that your wall is orthogonal to the x-y-plane. Then there are several options to extrude the floor without loosing "connection" e.g. lifting your wall up.

If your plane is level you can easily lock the extrude to a plane by Extruding and then (while the extrude is active) press shiftz this will lock the movement to the x-y-plane. In case you want the extrude to be rectangular you can press y during the extrude to lock it to the Y-Axis. (This can be a powerful technique if you are comfortable with the different coordinate system orientations in blender) Blender_Manual

The other method is, as pointed out in the comment, using vertex snapping with the target being a plane. https://www.blender.org/manual/editors/3dview/transform/transform_control/snap.html%3E