I am going to do exchange student program in Paris next month and also live for 9 months. Of course, I am just new there and wonder about the transportation service.
My question: I would like to know the comparison each transportation service with average expense in Paris (i.g. Taxi, public metro or etc)
Cheapest: walk everywhere.
Paris isn't a very nice place for biking (though it's improving, but slowly), but you can do it. There's a public short-term bike rental service called Vélib: you take a bike from one of the ubiquitous stands (only within the Paris city limits and in a short range outside, not in the whole suburbs) and bring it to another stand within half an hour. The yearly pass is 29€ and you can use store the Vélib pass on your Navigo card (see below).
For public transport (buses, metros, trains, trams: ticketing is unified), get a Navigo pass that covers the zones that you'll be traveling to (zone 1 is the Paris municipalities and zones 2–5 make concentric rings). During the week-end, you can travel everywhere in Île-de-France regardless of zones, so pick the zones you need during the week. Since you'll be a student, get the student pass: Imagine'R. In addition to being about half the price of a normal pass, a few places give discounts for it. You'll need to have some proof that you're a student in order to get the Carte Imagine'R, and you have to mail-order it, it's a bit of a hassle. You will need a photocopy or scan of your student card or attestation from the French university you'll be visiting. Imagine'R is valid for one year starting on the first of a month of your choice between September and December, and you have to send in your application at least 3 weeks before.
Taxi is mildly expensive and typically outside of a student's budget.
It depends where you are going to live in Paris. In terms of public transport I would say the most expensive form would be the taxi. The metro/bus/tram would cover all your transportation needs within the city boundaries. You could go for a monthly subscription or buy de "carnet de 10" tickets. These sets of 10 tickets you can buy at any vending machine.
As @Gilles already explained there is also the Velib, but I would advise you to buy a bicycle. I have to disagree with @Gilles, Paris is awesome for cycling. I spent 2 years living in Paris and my bicycle was my main form of transport. A lot of my colleagues back then called me an idiot because there is this huge misconception that cycling is a dangerous affair. On the contrary, there is one brilliant rule, which makes cycling the ultimate form of transport in Paris and that is that cyclists are allowed to use the bus lane. Nothing beats the sensation of cycling past traffic jams on a almost empty bus lane in Paris. To give you an idea. A fellow student lived in the same campus as me (Le cite universitaire). It took her 45 minutes by metro to get to the faculty building, while I only needed 10 minutes of cycling.
There is an awesome bicycle shop, where you can get nice second hand biccycles, or rent one to try if cycling paris is your cup of tea. (Gepetto velos)
