How does a newly-installed personal computer connected to an Ethernet discover the IP addresses of local servers? How does it translate them to Ethernet addresses?

What will be an ideal response?

The first part of the question is a little misleading. Neither Ethernet nor the Internet support ‘discovery’ services as such. A newly-installed computer must be configured with the domain names of any servers that it needs to access. The only exception is the DNS. Services such as BootP and DHCP enable a newly-connected host to acquire its own IP address and to obtain the IP addresses of one ore more local DNS servers. To obtain the IP addresses of other servers (e.g. SMTP, NFS, etc.) it must use their domain names. In Unix, the nslookup
command can be used to examine the database of domain names in the local DNS servers and a user can select approriate ones for use as servers.The domain names are translated to IP addresses by a simple DNS request.
The Address Resolution Protocol (ARP) provides the answer to the second part of the question. Each network type must implement ARP in its own way. The Ethernet and related networks use the combination of broadcasting and caching.