This mission is activated by pressing the correct button when or after being prompted when entering a Taxi, Cabbie, Kaufman Cab, or Zebra Cab. You can get an Ambulance from any of the four hospitals in Vice City, or by causing mayhem and racking up casualties.
The Taxi mission is a different take compared to the Paramedic, Firefighter and Vigilante Missions by the fact that it does not work off of a levelling system to complete it.
The aim is not set clearly to you, but your goal is to complete 100 fares. This does not have to be done all in one run - your total has to add up to 100. Therefore, you can do this as you go if you want.
The Strategy
The Taxi mission seems simple when outlined - pick up fares, and drop them off in the time limit. But there is more to it than that.
Issues
There are several issues to the Taxi mission, which can be bypassed by the good drivers, but it can be a problem for the inexperienced.
The main, principle issue is time. You are given time to get to the fare's destination, which will carry over onto the next fare. It is plainly obvious that being slow to get there will have you at a disadvantage. Therefore, time will not become an issue if you are a good driver.
The Taxi itself can become an issue if your driving isn't clean. If you damage your Taxi to the point of it smoking, the fare you had will be scared off, and any other potential fares won't want to be jumping into a wreck. If this happens, you will have to get to a Pay 'n' Spray before your time runs out, and then you will have to pick up another fare. Drive cleanly, and if you are around a Pay 'n' Spray looking for a fare and your Taxi is becoming a bit worse for wear, then repair it quickly.
Time and damage are the main issues here, but if you have an ounce of common sense and a feel for the streets and the cab you are driving, the mission is easy.
Advice
Like some of the missions in the game, the knowledge of the city is key. For me, the West Island/Mainland was best due to the open layout of the main streets and the fact that I spent most of my time there. Wherever you feel comfortable, you activate the mission in that area to attempt it.
If you are doing this for profit, then aim for a full run. Your tip is based on your driving and the time you took to get there. A faultless and fast run on a fare is profitable. Also, for every five fares you complete, you earn a bonus. This starts at $500, and goes up $500 for every five fares after that. On my playthrough of this mission, I was able to complete 100 fares in one go, finishing up with over an hour's worth of time and earning over $100,000. If you absolutely ace this mission, you will earn a lot of money for this.
The best vehicle for this mission is the regular Taxi. With it being a modern sedan, it is sturdy and the suspension is better than the other three cabs you can use. If you can compensate for a dodgy suspension, then you can use it, but past experience makes the Taxi my recommendation for it.
Reward
Your reward, apart from money, is the "Hop" feature in all Taxi cabs. When you try to activate the horn, the Taxi cab will spring up, allowing you to gain height and perform some weird and wonderful stunts.