It looks like I made an unlucky choice with my new Wireless adapter Ovislink Airlive WN-370USB. It just doesn't come up.
There are confusing information about the driver module for it on the "google". All that I found out about it is this:

OS and HW specification:
Slackware64-current - kernel 2.6.38.7

Airlive WN-370USB:
New USB device found, idVendor=1b75, idProduct=8171
New USB device strings: Mfr=1, Product=2, SerialNumber=3
Product: AirLive WN-370USB Adapter
Manufacturer: Manufacturer Realtek
SerialNumber: 00e04c000001

I find this possible drivers for my device:
http://www.wikidevi.com/wiki/OvisLink_WN-370USB

The windows driver contain these files net8192su.inf and rtl8192su.sys.

I tried to load the next modules but nothing changes
Is there something more to be done after this or it just means that it won't work (if I cannot see wlan0 device after the modprobe with ifconfig -a)

Check the logs for the error messages - make sure no other driver modules are being loaded that are blocking. You may also need firmware.
You could try using NDISwrapper. I used to use it for a Phillips adapter successfully. It wraps the Windows driver so GNU/Linux can use it. Bit of a cop-out but it does work (well, it did for me ,anyway)