I tried to install arch Linux on my laptop, and I have messed up somehow. This is what I get...
error: no such device: a0b8124e-507a-4c5a-bfc9-79e306898aa2.
Entering rescue mode...
Grub rescue> ls
(hd0)
Grub rescue>ls (hd0)
(hd0): Filesystem is unknown.
Grub rescue>

Since you only got as far as first reboot, you might try starting over (carefully) from scratch. Make sure that you do not skip any steps. I also always label disks, and use the label in grub, fstab, etc. but that would be overkill for your issue.

BTW: what it APPEARS is going on is that the UUID for the disk as used in grub (perhaps in stage-1) does not match the UUID on the disk. This can happen if the disk was re-established with a new UUID, but grub was not fully and correctly written after. There are other things that can cause this, and other ways it can happen, but I am NOT an expert on that, I just read about them happening to others. (Been very lucky that way since pre Fedora days, knock wood.)

Run:
update-grub
and next:
grub-install /dev/sda (replace sda with your boot drive if needed)

... and don't use partition numbers.