install drivers for usb wifi adapter (RT5370 chipset):

apt install firmware-ralink


-----

quick-setup (https://raspberrypi.stackexchange.com/a/108593):


# create interface file for a wired connection

sudo -Es
cat > /etc/systemd/network/04-wired.network <<EOF
[Match]
Name=e*

[Network]
## Uncomment only one option block
# Option: using a DHCP server and multicast DNS
LLMNR=no
LinkLocalAddressing=no
MulticastDNS=yes
DHCP=ipv4

# Option: using link-local ip addresses and multicast DNS
#LLMNR=no
#LinkLocalAddressing=yes
#MulticastDNS=yes

# Option: using static ip address and multicast DNS
# (example, use your settings)
#Address=192.168.50.60/24
#Gateway=192.168.50.1
#DNS=84.200.69.80 1.1.1.1
#MulticastDNS=yes
EOF


# deinstall classic networking

sudo -Es
apt --autoremove purge ifupdown dhcpcd5 isc-dhcp-client isc-dhcp-common rsyslog
apt-mark hold ifupdown dhcpcd5 isc-dhcp-client isc-dhcp-common rsyslog raspberrypi-net-mods openresolv
rm -r /etc/network /etc/dhcp


# setup/enable systemd-resolved and systemd-networkd

apt --autoremove purge avahi-daemon
apt-mark hold avahi-daemon libnss-mdns
apt install libnss-resolve
ln -sf /run/systemd/resolve/stub-resolv.conf /etc/resolv.conf
systemctl enable systemd-networkd.service systemd-resolved.service
exit


# configure wpa_supplicant for wlan1 as access point

sudo -Es
apt install rfkill
cat > /etc/wpa_supplicant/wpa_supplicant-wlan0.conf <<EOF
ctrl_interface=DIR=/var/run/wpa_supplicant GROUP=netdev
update_config=1

network={
    ssid="peach"
    mode=2
    key_mgmt=WPA-PSK
    psk="cloudless"
    frequency=2412
}
EOF
chmod 600 /etc/wpa_supplicant/wpa_supplicant-wlan1.conf
systemctl disable wpa_supplicant.service
systemctl enable wpa_supplicant@wlan1.service
rfkill unblock 1

# configure wpa_supplicant for wlan0 as client

cat > /etc/wpa_supplicant/wpa_supplicant-wlan1.conf <<EOF
ctrl_interface=DIR=/var/run/wpa_supplicant GROUP=netdev
update_config=1

network={
    ssid="TestNet"
    psk="anotherSecretPassword"
}
EOF
chmod 600 /etc/wpa_supplicant/wpa_supplicant-wlan0.conf
systemctl disable wpa_supplicant.service
systemctl enable wpa_supplicant@wlan0.service
rfkill unblock 0


# configure interfaces

cat > /etc/systemd/network/08-wlan1.network <<EOF
[Match]
Name=wlan1
[Network]
Address=11.11.11.1/24
# IPMasquerade is doing NAT
#IPMasquerade=yes
#IPForward=yes
DHCPServer=yes
[DHCPServer]
DNS=84.200.69.80 1.1.1.1
EOF

cat > /etc/systemd/network/12-wlan0.network <<EOF
[Match]
Name=wlan0
[Network]
DHCP=yes
EOF