The usual way is to leave the wire bare and arrange it on ceramic insulators. In some lower temperature applications it can be sleeved with teflon or silicone tubing.
I tried lots of materials, but only two worked: ceramic and mica. Mica is better, but more fragile to work with. For ceramic, I bought some small tile pieces at Lowe's and used a diamond point drill to penetrate them. Either way, you then face the problem of connecting the nichrome to the copper feed wires. I ended up using mechanical (e.g., nut and bolt) connections.
You can also wind a coil on a bolt, and then turn the coil off the bolt, and let air be your insulation. Just don't let the turns touch or your resistance will be lowered. Here's a good introduction.