cleaner notifications

How do you set up notifications of bookings and cancellations to cleaning staff?

It may be worthwhile reading through this article if you haven't already:

https://www.ownerrez.com/support/articles/bookings-display-for-cleaners#portal-access

Here's a key excerpt from that article:

You can create a trigger email in OwnerRez that sends a customized email template (that you create) which only shows the departure day. Something like "Guest departing tomorrow (May 14)" which is sent 1 day before departure, or one that sends immediately when the booking is created.  This would notify the cleaner when a guest is departing so they know the property needs to be cleaned.
 
Similarly, you can create a custom email template and trigger for cancellations, with trigger criteria specifying that it should only be sent in the event of a booking cancellation.

How can I make it so the cleaner gets a text alert of a new booking? 

If you have SMS enabled, simply setup an SMS template and trigger. Hard code the cleaner's phone number in the template. You could put something like this:

New Booking:
{PDISPNAME}

{BARRDAY} {BARR} to {BDEPDAY} {BDEP} for {BNNGHTS} nights

{CFULL}

{CEMAILPRIME}

{CPHONEPR}

{BNGUEST} guests, {BNADULT} adults and {BNCHILD} children, plus {BNPET} pets

Booked via {BSOURCE}