I paid around $110 for the frame, $40 for cables, $100 for brakes, $400-500 for high-end wheels (Shimano XTR hubs, Velocity Synergy OC rims, DT Swiss Competition spokes, brass nipples, and Shimano XT centerlock brake rotors), and then used a groupset I had sitting in a box. If you want to buy brand-new parts, I expect it'd probably cost $800-1000 by the time you're done. And that's for relatively low-end stuff. If you're willing to accept used parts, you can save a ton of money. Buying a used bike and stripping components from it can be a great way to get a new bike going, assuming you're starting with quality components in decent shape. You could also move components from your current bike over, perhaps with a few upgrades (e.g. shifters, front derailleur, crank) along the way, and save money.

Best thing to do is put together a parts list and start shopping: handlebars, bar tape/grips, stem, headset, headset spacers, shifters, brake levers, cables, front derailleur, front brake, rear derailleur, rear brake, bottom bracket, crankset, pedals, cassette, wheels, chain. Don't forget all the "accessories": bottle cages, fenders, racks, etc.