How to find speed of wlan interface?

You can use the iwconfig tool to find this info out:

$ iwconfig wlan0
wlan0     IEEE 802.11bg  ESSID:"SECRETSSID"  
          Mode:Managed  Frequency:2.462 GHz  Access Point: 00:10:7A:93:AE:BF   
          Bit Rate=48 Mb/s   Tx-Power=14 dBm   
          Retry  long limit:7   RTS thr:off   Fragment thr:off
          Power Management:off
          Link Quality=55/70  Signal level=-55 dBm  
          Rx invalid nwid:0  Rx invalid crypt:0  Rx invalid frag:0
          Tx excessive retries:0  Invalid misc:0   Missed beacon:0

If you want the bit rate from /sys directly try this:

$ cat /sys/class/net/wlan0/wireless/link
51

Or from /proc:

$ cat /proc/net/wireless 
Inter-| sta-|   Quality        |   Discarded packets               | Missed | WE
 face | tus | link level noise |  nwid  crypt   frag  retry   misc | beacon | 22
 wlan0: 0000   56.  -54.  -256        0      0      0      0      0        0

NOTE: The value for the link in the 2nd example is 56, for e.g.

I believe the MB/s is a calculated value, so it won't be stored anywhere specifically for the wlan0 device. I think it's taking the aggregate bits transferred over the interface and dividing it by the time it took said data to be transferred.

One additional way to get this information is using the tool iw. This tool ew nl80211 based CLI configuration utility for wireless devices. It should be on any recent Linux distro.

$ iw dev wlan0 link
Connected to 00:10:7A:93:AE:BF (on wlan0)
    SSID: SECRETSSID
    freq: 2462
    RX: 89045514 bytes (194863 packets)
    TX: 34783321 bytes (164504 packets)
    signal: -54 dBm
    tx bitrate: 48.0 MBit/s

This also shows the amount of sent and received packets (RX/TX).

The approach by slm is wrong, the data rate shown by iwconfig is the max speed supported by the interface for the link. It's not the current at which data is transferred. Use the /sys/class/net/<interfacename>/statistics/<tx/rx>_bytes file to get per interface bytes transferred live.