As others have said, CCNA study materials are probably a good start.
If you want to start understanding the point of of ASNs and BGP, this page isn't bad: https://www.cloudflare.com/en-gb/learning/network-layer/what...
Given what you've described about your task, you probably only need to learn TCP/IP, and don't need to learn about the lower layers (what the OSI model calls the physical and data link layer) or the upper ones (e.g. you probably don't care about whether your routers are carrying HTTP, SMTP or whatever).
Internet: collection of LANs
MAC address: the hardware address that uniquely identifies a network card, but is only visible to other devices on the same LAN
IP address: an address that uniquely identifies a device on the internet
Subnet: a subset of the IP address space, that's used for a LAN
DHCP: the protocol routers use to assign an IP address to each device on the LAN
ARP: the protocol used by a device on a LAN to find another device on the same LAN, when it knows the IP address but needs the MAC address. (You need the MAC address to send a packet to a device on your LAN)
Router: has more than one network interface, with each interface on a different network. At home, your router is connected to your LAN, and to your ISPs network.
ASN: A network that has a permanent allocation of part of the IP addr as space.
BGP: the protocol used for one router to tell another router what networks it can route traffic to.
How do you send traffic to devices when you aren't on the same LAN? You send them to your router (whose IP address you find out when you're assigned an IP address via DHCP, and whose MAC address you can find using ARP).