Hey, I learned a long time ago, there are no stupid questions. The top was flared out over the horn of an anvil, striking from the outside. Start at the initial necking down area and working (pushing metal) toward the end, flaring as you go. This will take several annealings to get the flare where you want it. You'll hear and feel when you need to anneal. You need to hold the vase at an angle to horn to create the flare....more angle more flare. Here is a rough drawing of what I mean:

flaring top: flaring the top of the vase

Thanks for the info. I just starterd doing metal art last year. I will post some pics of some of the stuff I have made.