Charles Xavier's father was a "wealthy nuclear scientist". In the beginning, Charles personally bankrolled the Xavier Institute/X-Men using his family's money.
This included, but was not limited to things like upgrading the mansion to house the training levels, providing a helicopter (the predecessor to the Blackbird jet), providing and replacing uniforms, providing health care for injured students, and rebuilding/repairing the mansion and parts of the Danger Room repeatedly.
These have all been recurring costs. The mansion has been damaged or outright destroyed a ridiculous number of times. X-Men can't get into a fight without someone's uniform getting damaged.
In one of the more recent stories (I believe it was an early issue of Wolverine & The X-Men), a comment is made about how the X-Men are pretty much bankrupt.
Where has all this money come from over all these years?
Xavier may have had a large war chest to start with, but no other income has ever been mentioned to my knowledge. Student's tuition could account for some of it, but there's no way that's going to fund everything.