Seems I don't have permission to edit the wiki.  Here are the verified steps:
On your computer (not on the Pi):
    - Download piCore-9.0.1
    - Copy the image to the SD card (see instructions on the wiki)
    - Expand the second partition, e.g. in Ubuntu:
        $ sudo fdisk /dev/sdb
        [sudo] password for rob: 
        Welcome to fdisk (util-linux 2.27.1).
        Changes will remain in memory only, until you decide to write them.
        Be careful before using the write command.
        Command (m for help): p
        Disk /dev/sdb: 14.5 GiB, 15523119104 bytes, 30318592 sectors
        Units: sectors of 1 * 512 = 512 bytes
        Sector size (logical/physical): 512 bytes / 512 bytes
        I/O size (minimum/optimal): 512 bytes / 512 bytes
        Disklabel type: dos
        Disk identifier: 0x0009bf4f
        Device     Boot Start    End Sectors Size Id Type
        /dev/sdb1        8192  77823   69632  34M  c W95 FAT32 (LBA)
        /dev/sdb2       77824 100351   22528  11M 83 Linux
        Command (m for help): d
        Partition number (1,2, default 2): 2
        Partition 2 has been deleted.
        Command (m for help): n
        Partition type
           p   primary (1 primary, 0 extended, 3 free)
           e   extended (container for logical partitions)
        Select (default p): p
        Partition number (2-4, default 2): 
        First sector (2048-30318591, default 2048): 77824
        Last sector, +sectors or +size{K,M,G,T,P} (77824-30318591, default 30318591): 
        Created a new partition 2 of type 'Linux' and of size 14.4 GiB.
        Command (m for help): w
        The partition table has been altered.
        Calling ioctl() to re-read partition table.
        Synching disks.
    - Note that 77824 is the important figure above - it's the start sector of the second partition and must be entered when recreating the partition.  Default values are ok for other inputs.
    - Resize the filesystem to fit the newly-expanded partition, e.g. in Ubuntu:
        $ sudo resize2fs /dev/sdb2
        resize2fs 1.42.13 (17-May-2015)
        Please run 'e2fsck -f /dev/sdb2' first.
        $ sudo e2fsck -f /dev/sdb2
        e2fsck 1.42.13 (17-May-2015)
        Pass 1: Checking inodes, blocks, and sizes
        Pass 2: Checking directory structure
        Pass 3: Checking directory connectivity
        Pass 4: Checking reference counts
        Pass 5: Checking group summary information
        /dev/sdb2: 55/2816 files (1.8% non-contiguous), 9660/11264 blocks
        $ sudo resize2fs /dev/sdb2
        resize2fs 1.42.13 (17-May-2015)
        Resizing the filesystem on /dev/sdb2 to 15120384 (1k) blocks.
        The filesystem on /dev/sdb2 is now 15120384 (1k) blocks long.
    - Mount the second partition:
        - e.g. on Ubuntu desktop by clicking its icon in the dock
        - there should be a "tce" directory at the top level
        - find its mount point and cd to "tce/optional" in a terminal
    - Download the extra files required:
        - (you may have to do this as root, depending on the mount permissions)
        - for pkg in ca-certificates libiw libnl ncurses openssl readline wifi wireless-4.9.22-piCore wireless_tools wpa_supplicant firmware-rpi3-wireless; do for f in $pkg.tcz{,.dep,.md5.txt}; do wget 
http://ftp.nluug.nl/os/Linux/distr/tinycorelinux/9.x/armv6/tcz/$f; done; done
        - fix up file ownership and permissions:
            - $ chown 1001:staff *.tcz*
            - $ chmod 664 *.tcz*
    - Unmount the SD card
    - Transfer SD card to the Pi Zero W
On the Pi Zero W (attach a monitor and keyboard...):
    - $ tce-load -i firmware-rpi3-wireless
    - $ echo "firmware-rpi3-wireless.tcz" >> /mnt/mmcblk0p2/tce/onboot.lst
    - $ sudo reboot
    - time passes...
    - $ tce-load -i wifi > /tmp/tce-load-wifi.log
    - $ sed "s,:.*,," /tmp/tce-load-wifi.log >> /mnt/mmcblk0p2/tce/onboot.lst
    - $ sudo wifi.sh
        - select a wifi AP and enter password
    - $ ifconfig
        - should now list wlan0 with an IP address
        - wifi.db has been created in the home dir, but this is a temporary location
    - if you reboot at this point, you'll have to redo the wifi.sh step
    - $ echo "sudo wifi.sh -a" >> /opt/bootlocal.sh
    - $ filetool.sh -b
        - to save bootlocal.sh and wifi.db into persistent storage
After this, after every reboot the Pi will connect to wifi automatically.
Rob.