dmesg |grep eth0

mii-tool -v  eth0

ethtool eth0

ethtool - Display or change ethernet card settings

sudo apt-get install ethtool

Settings for eth0:
    Supported ports: [ TP ]
    Supported link modes:   10baseT/Half 10baseT/Full
                            100baseT/Half 100baseT/Full
                            1000baseT/Full
    Supported pause frame use: No
    Supports auto-negotiation: Yes
    Advertised link modes:  10baseT/Half 10baseT/Full
                            100baseT/Half 100baseT/Full
                            1000baseT/Full
    Advertised pause frame use: No
    Advertised auto-negotiation: Yes
    Speed: 1000Mb/s
    Duplex: Full
    Port: Twisted Pair
    PHYAD: 0
    Transceiver: internal
    Auto-negotiation: on
    MDI-X: Unknown
    Supports Wake-on: d
    Wake-on: d
    Current message level: 0x00000007 (7)
                   drv probe link
    Link detected: yes

cat /sys/class/net/<interface>/speed