What's needed to wirelessly connect two offices 100 feet apart?

If you have a free Ethernet port on the LAN side of your wireless router, that's where you'll start your cable...

run to the office 100 feet away. (If all your existing router's LAN ports are occupied, "add" ports by dropping another small switch from an existing LAN port.) Since part of that Ethernet cable is going outside, use outdoor-grade bridging cable instead of "regular" indoor Cat5 cable. Consider whether you need to lay conduit as well.

What goes at the far end of that cable run? If all the users in the new office are wireless, you could simply place an AP in that office, connecting the Ethernet port of the AP to the long cable run from the home office. This configuration is simple, but makes those new users depend on the wireless router in the home office for DHCP services. Alternatively, you could place another wireless router in that office, connecting the WAN port of the new router to the long cable run from the home office. This catch here is that print services are easier to share in a single LAN (AP) than across subnets (routers). Finally, if one or more users in the new office will be wired devices, use an AP or router with a few built-in LAN ports.

Your new AP/router and your existing router form two separate wireless LANs, with wired connectivity between them. If you go with a simple AP, you can give the new AP the same network name (ESSID) as your existing router so that stations can roam between them without reconfiguration. If you use a wireless router in the new building, it may be best to give the new device a different ESSID, since each building will have its own subnet with its own IP addresses, and roaming is likely to cause application interruption.