About what hardware is installed you could use those commands (as root), lspci and lsusb. Dmesg is also a good starting point.
As you are using Ubuntu surely your hardware will be recognized without any problem, but if not, you need to know how system recognizes both cards.
For example, from my lspci -v I get:
0000:00:09.0 Ethernet controller: Realtek Semiconductor Co., Ltd. RTL-8139/8139C/8139C+ (rev 10)
Subsystem: Surecom Technology EP-320X-R
Flags: bus master, medium devsel, latency 32, IRQ 11
I/O ports at e400 [size=256]
Memory at ef012000 (32-bit, non-prefetchable) [size=256]
Capabilities:  Power Management version 2
[17179590.808000] eth0: RealTek RTL8139 at 0xd088c000, 00:02:44:52:6a:db, IRQ 11
[17179590.808000] eth0: Identified 8139 chip type 'RTL-8100B/8139D'
So, for my Realtek card I know that my system will use eth0.
From here, ifconfig to configure the cards.