I can't say that both answers above are wrong but I feel that they are hard to understand, at least for me.

However, yes, ARP is used but there is 2 cases that you can't "really" dismiss and they are the following:

1. The destination is within the source's LAN: in this case, thr source will send a broadcast message with all 1s turned on or Fs in hex (ff:ff:ff:ff:ff:ff) with its IP and Mac addresses (source info), and it will fill the destination IP and keep the "destination"'s MAC accress null or different words, it says (Hello "All", I've sent you all a message, the one of you holding this IP address [destination IP address] please reply to me. The only device that will reply back to the ARP Request with an ARP Reply is the device holding that Mac address.

2. When the destination is in a different network (router, internetwork, remember?), it will be forwarded to the defaultn gateway (the directly connected interface's IP), the router will then forward it to the concerned network segment based on the IP address of the destination that is filled in the ARP Requet, the destination in that network segment will reply with an ARP Reply to the source filling his Mac address.

I hope this was helpful!
and please, correct me if I am wrong