Once you have booted from the Alpine Linux installer CD and logged in using root / <no password> as described in What is the Alpine linux default login & password?, one often wants to test if DHCP works before going through the installer and potentially having to repeat the process.
First enable Ethernet using
ifconfig eth0 up
Then run the DHCP client using
udhcpc eth0
This will show you the IP address of the lease that your Alpine Live CD did acquire.