Probably a lot. I'd say close to a million. You have to hire people, manage the business and buy equipment.
Making a mining buisness would take millions - land to make a mine, staff, headquarters, equipment etc..... But the profit you could make would be a handsome reward. But unless you already own a buisness or are a millionaire I would steer away from the mining industry.
A few million at least it costs a lot of money to start a mine. You need your employees miners digging equipment land ect. the list goes on and on. Not to mention that most mines dig up metals at a loss. Very few mining companies actually make a decent profit.
Check out the show "Gold Rush" on the Discovery Channel. They follow small mining companies on their ventures. It's really very interesting. You can see some clips here... http://dsc.discovery.com/tv/gold-rush-alaska/
There are certain factors that needs consideration when you open up a business like mining. First, location. If you want to put up mining business overseas, government share is a consideration plus permit, engineers, workers, and so forth. Just like the rest who posted here, it needed millions to operate depending on how big the perimeter of that prospective area is.