it usually depends on how busy they are and if someone's in the area.
the last time i phoned (non-emergency) there was someone up within 20 minutes to see him.
phone and ask - they will usually phone you back and let you know
Usually you have to book an appointment for when they are in the area.
They wont come same day unless they are five mins down the road or its an emergency.
For vaccs and other routine issues I usually phone for an appt a week in advance, but if I have an emergency my vet has always been able to come out that day.
For vaccs etc I book an appointment. For anything unexpected (not necc. an emergency, but something that needs prescription drugs) the vet comes the same day.