To create a volcano you need to be in a place where magma from the mantle is capable of reaching the surface.
This can happen at:
- divergent tectonic plaque borders (i.e. Iceland)
- convergent tectonic plaque borders (i.e. Japan or Andes)
- volcanic hot spots (i.e. Hawaii)
Coincidentally those places are also where you can find natural volcanoes. But you want an artificial one, quick and cheap.
I suggest you dig some high yield nukes at Yellowstone caldera, and detonate them to weaken the crust. Rinse and repeat.
The place is already like a shaken champagne bottle, the nukes would be like tapping the cork. You would get a nice KABOOM, you won't need to spread the news that the experiment is successful, meters of volcanic ashes will the entire North America that you did it!
The last supereruption of the Yellowstone Caldera, the Lava Creek eruption (approximately 640,000 years ago), ejected approximately 240 cubic miles (1,000 $km^3$) of rock, dust and volcanic ash into the atmosphere.
A study published in GSA Today, the monthly news and science magazine of the Geological Society of America, identified three fault zones on which future eruptions are most likely to be centered. Two of those areas are associated with lava flows aged 174,000–70,000 years, and the third is a focus of present-day seismicity.
Note: considering that in any case you have to dig kilometers of rock, the use of nuke seems to be the only way to quickly dig down. Since you are not worried about the stability of the hole you are creating, at least.