First, you need to work with editable polygon objects, or with an edit poly modfier. Avoid editable mesh, because that's more of a legacy mesh format, and lacks many functions of editable polygon.
To pull new edges out, like he does in that video, just hold down shift on the keyboard while you pull a border edge, in edge subobject mode. It's called "edge extension" modeling. Works the same also in border subobject mode.
At the end, it appears he's using "soft selection" in vertex sub-object mode to pull the handle up and down, and the bowl of the spoon to shape it. There's a lot of ways to do that in Max, however. I use the Move brush in the Graphite Freeform tab, to do similar soft selection sculpting, without having to be in subobject mode, but learn the basics first, before trying that.
Personally, I think that video is too fast, and not a good learning tool. Find better tutorial videos, which are at normal pace, if you want to learn quickly.
