Todo: Was the raspberrypi-libs package renamed... or is it even still required?

Install the necessary firmware

apk add linux-firmware-brcm raspberrypi-libs

Install hostapd and dnsmasq

apk add hostapd dnsmasq

Configure /etc/hostapd/hostapd.conf

interface=wlan0
driver=nl80211
ssid=Pi3-AP
hw_mode=g
channel=1
macaddr_acl=0
auth_algs=1
wpa=2
wpa_key_mgmt=WPA-PSK
wpa_passphrase=raspberry
rsn_pairwise=CCMP
wpa_pairwise=CCMP

Configure your /etc/dnsmasq.conf

interface=wlan0
dhcp-range=10.0.0.2,10.0.0.5,255.255.255.0,12h

Configure Static ips for wlan0 in the file /etc/network/interfaces

auto wlan0
iface wlan0 inet static
  address 10.0.0.1
  netmask 255.255.255.0

Start the services

service dnsmasq start
service hostapd start

Enable the Services permanently on every bootup

rc-update add dnsmasq     
rc-update add hostapd

(to del)

rc-update del dnsmasq     
rc-update del hostapd

(or)

rc-update add dnsmasq boot    
rc-update add hostapd boot

(to del)

rc-update del dnsmasq boot    
rc-update del hostapd boot

Commit all changes to files

Make sure you run the command shown below to commit all changes, otherwise they will be lost on reboot.

lbu ci

References

https://gist.github.com/atlury/fe0ea8b91a981c103df7

https://frillip.com/using-your-raspberry-pi-3-as-a-wifi-access-point-with-hostapd/^{[Dead Link]}

Thanks oneinsect@gmail.com