There are many taxi companies in Regina. Some do well with telephone reservations, others have stands at major shopping malls or hotels. If you are not in Regina , the city, use a taxi company based in the city where you are staying or visiting... they'll usually be quicker to pick you up.
You can usually get around downtown for around $3-$5. Trips between downtown and the Airport are about $8-$9, definitely one of the cheapest rides in Canada.
Oh, yes, and if your driver was courteous and helpful, it is the custom to tip him (or her)! Tips on tipping.
Find Local Taxi cab companies.