Knoppix used to support :
1) Saving settings on local hard disk
2) Installation onto HD (at which point it becomes a Debian variant)
Have a look at the The Linux Wireless LAN Howto
http://www.hpl.hp.com/personal/Jean_Tourrilhes/Linux/ and do ask questions if there's stuff you don't follow.
I've seen recent discussions about W-LAN support and troubles with I think Realtek that got sorted out. Knoppix 5.1.1 may actually be too old to benefit from that. I have vague memories of NDIS wrappers working well using drivers intended for older Windows versions.
What is solid experience based advice, when choosing a driver prefer :
1) Linux kernel driver (if it works eg) ne2k-pci, e100, forcedeth etc)
2) Linux source driver, provided by Vendor or other support
3) A well supported Vendor driver with a wrapper (if it works eg) Nvidia 3D drivers)
4) Linux kernel wrapper (running binary driver for other system eg) NDIS)
5) Knock off Vendor binary driver that works, but will be a pain when you want to upgrade kernel
Linux doesn't have a stable Driver ABI, but unfortunately some vendors ticking boxes, for commercial-political reasons don't want to introduce source, nor assist kernel developers writing drivers for their products.
Best to buy products with Linux friendly manufacturers submitting source drivers for kernel inclusion, but when this is not the case, choose drivers with care and only use mystery binary modules as last resort. In past they not only have been a maintenance problem for Admin, but caused instability on machine, and with tainted kernel your problem becomes impossible to debug.