The way described by Oko is the best way, install OpenBSD onto the USB drive (..including bsd.rd) and you should be able to boot the device on any other system, baring any unforeseen problems.. USB booting isn't perfect.
If you already have an existing installing, you can prepare the device using
fdisk(8)/
disklabel(8),
newfs(8) and
installboot(8).
Vague example, do not copy paste.. you risk all your drives.. read the manuals.
$ sudo fdisk -e /dev/rsd?c
[...]
$ sudo disklabel -E /dev/rsd?c
[...]
$ sudo newfs /dev/rsd?a
$ sudo mount /dev/sd?a /mnt
$ sudo cp /boot /mnt; sudo cp /bsd.rd /mnt/bsd
This would be a good time to make a directory on the device for the installations sets, kernels and perhaps a few packages.
Finally,
$ sudo /usr/mdec/installboot -v /mnt/boot /usr/mdec/biosboot /dev/rsd?c
Have fun.