How are MAC addresses used in routing packets?
ip, tcp
Solution
IP packets aren't always encapsulated in Ethernet frames. There are other physical media such as ISDN, etc. When packets are routed, IP addresses are used to determine the next hop and the physical address is used to physically identify the interface serving as the next hop. Only the former (determining next-hop) is usually called routing.
To answer your second part, MAC addresses are discovered through ARP (Address Resolution Protocol) in IPv4 & ND6 (Neighbor Discovery) in IPv6.
Update: The destination IP address in the IP header is the final destination. In the process of routing (at each hop), you get the next hop's IP address to (eventually) reach the final destination from the routing table (this could be a default gateway's IP address). To send the packet to the next hop, you need its MAC address. While hopping through intermediate links, the IP address in the IP header don't change - only the MAC addresses change.
Problem
I recently found that packets are encapsulated within ethernet frames. Packets use IP addresses, frames use MAC addresses. Why aren't IP addresses used in ethernet frames for routing? I understand that when trying to access a basic website, the computer goes to a DNS to find the IP address relevant to the user-entered domain name. How do computers find the correct MAC address? Really, how are MAC addresses used in routing internet traffic? Thanks