Get started:
Image a micro SD card and boot up with it on the Pi Zero W.
Set the password to something besides raspberry. (THIS IS IMPORTANT!)
Use raspi-config to turn on the ssh server.
We need to get a working Internet connection via WiFi:
Edit the /etc/network/interfaces file so that the wlan0 section looks like the 5 lines below. Replace SSID and PASSWORD with the values needed for your Internet access point:
auto wlan0
iface wlan0 inet dhcp
wpa-ssid SSID
wpa-psk PASSWORD
Reboot and make sure you can access the Internet from the Pi.
The Pi also needs to become an access point:
Run the following command: sudo apt-get install hostapd dnsmasq
Add the following 3 lines to the /etc/dnsmasq.conf file:
interface=lo,uap0
no-dhcp-interface=lo,wlan0
dhcp-range=192.168.2.100,192.168.2.200,12h
 Create the /etc/hostapd/hostapd.conf file and add the following 12 lines to it. Change SSID and PASSWORD to what you want them to be. Also, change 6 to the channel that your Internet access point is operating on. Use the command: "sudo iwlist wlan0 channel | grep Freq" to find out what it is:
interface=uap0
ssid=SSID
hw_mode=g
channel=6
macaddr_acl=0
auth_algs=1
ignore_broadcast_ssid=0
wpa=2
wpa_passphrase=PASSWORD
wpa_key_mgmt=WPA-PSK
wpa_pairwise=TKIP
rsn_pairwise=CCMP
Add the following 4 lines to the /etc/network/interfaces file:
auto uap0
iface uap0 inet static
address 192.168.2.1
netmask 255.255.255.0
Add the following 6 lines to the /etc/rc.local file:
iw dev wlan0 interface add uap0 type __ap
service dnsmasq restart
sysctl net.ipv4.ip_forward=1
iptables -t nat -A POSTROUTING -s 192.168.2.0/24 ! -d 192.168.2.0/24 -j MASQUERADE
ifup uap0
hostapd /etc/hostapd/hostapd.conf &
Only allow SSH access to the Pi from the wireless interface:
Add the following line to the /etc/ssh/sshd_conf file:
ListenAddress 192.168.2.1:22
Finish up and test:
Reboot.
From another computer, connect to the Pi via WiFi using the SSID and password you set up in the hostapd.conf file.
You should now be able to access the Internet from that computer. Your network traffic is flowing through the Pi to your access point!
You should also be able to access the Pi via SSH at address 192.168.2.1 if you need to configure anything.
I want to give credit to anthony19114 for his forum posting at: https://www.raspberrypi.org/forums/viewtopic.php?t=138730. His instructions were the most complete I was able to find.