Safety

I wouldn't say Paris is dangerous for your life.

For your goods, read the list of common scams in Paris.
Beware of pickpockets in metro and touristic places. Don't show your expensive smartphone. Hold it strongly with two hands. Don't stay near a door while using it.
The most annoying are the young gipsy girls pretending to be deaf, they show you a paper they want you to sign and scam some money, and pickpocket you at the same time.
In Montmartre, black guys try to lace a string around your wrist and then ask for payment, just walk away.

Moving

If you have a smartphone, install an offline map app like maps.me, then download Paris/Île-de-France map.
The app CityMapper is pretty good too.

Metro

For travel to/from other cities, see Cheap travel from Paris

http://ratp.fr is the official website

(Prices may change regularly, usually once a year)

RER inside Paris (zone 1) and metro (all lines, even outside of Paris) is always the same price: 1 ticket. You can use the same ticket changing metro and RER.
Tramway and bus also. You can use the same ticket changing tram and bus.
But you can't use the same ticket changing metro and bus.

1 metro ticket at a yellow machine is 1.90 €
(Buying a ticket in the bus costs 2 € and doesn't allow you to change to bus or tram)
10 metro tickets cost 14.90 €
On saturday, sunday and public holidays, people under 26 can buy a day ticket (zone 1-3) for 3.85 €

Paris is very small, you can walk between most places, don't buy an expensive all-day pass (7 € for one day, only worth it if you take the metro > 5 times).
If you stay from monday to sunday, a Pass Navigo découverte could be interesting: the card costs 5 € then you can load it for one week (Mon-Sun) for 21.25 € or one month (01 to 30-31) for 70 €, and it's all zones. Buying it at CDG is already 10 € saved.

RER outside Paris depends on the zone you go. Versailles is the main touristic thing to see outside of Paris.

Coming from airport

While you're at the airport, ask for a free Paris paper map at an info booth.

Roissy CDG

CDG ratp page
The best option is to take the RER B (10.30 €), then you can take the metro with the same ticket.
There is a cheapest way but not worth it, take the bus 350 or 351 that cost 3 tickets and take 1 h 20, then you have to pay a new ticket to take the metro.

Orly ORY

Orly ratp page
Take tram 7 with one ticket, then take metro 7 with another ticket (then any metro with the same ticket).

Beauvais BVA

The usual solution is the 17 € bus that will bring you in Porte Maillot. Then take the metro or walk 1 km to see Arc de Triomphe.
Beauvais train station is 5 km from the airport, take an unfrequent bus or walk 1 h if you want to take the train, which will be the same price as the bus except if you have a discount.
You can try to find a car-sharing on blablacar.com around 7-8 €
Or even hitchhiking if the weather is good and you have some time, there is an easy spot with a stop sign route de l'aéroport / rue de l'île de France almost every car pass by. If it fails there is always the bus (check the times).
You can not sleep at Beauvais airport, it closes at night.

Bicycle

Velib is an automated bicycle rental with stations, you need a credit card, when you put it back be sure you get the stop logo (then you can take it again).
The day ticket costs 5 €, 7-day ticket 15 €, includes unlimited 30-min rides on mechanical (green) bicycles ; electric (blue) bicycles are available but 1 € each ride.
Check out where the stations are, the Citymapper app displays them and the number of bicycles and spots.
Be careful the 300 € deposit could be blocked up to 30 days if you have a foreign card (like Visa Electron or Maestro). And lost if you don't put back the bike correctly.

There are free-floating bikes and motorized scooters at 1 € to start + 0.15 € / min, quite expensive.

Food

Lidl is the cheapest, but there are only 20 and not in the center.
Carrefour, U express, Franprix are normally-priced, you can find a lot of them, closing time depend, between 20:00 and 22:00.
You can also find G20, Monoprix, A2pas.
The bigger the cheaper, but biggest supermarkets are not in the center.
Some supermarkets offer a discount on food out-of-date today or tomorrow, it's either written on the box or you can ask the cashier.
On sunday afternoon most of supermarkets are closed.
The small shops ("épicérie", "alimentation générale") open day and night are expensive.

Attractions

A lot of museums and other attractions are free if you are under 26 and from European Union or living in it.
If you're < 26 but not from Europe or living here, you can still try to show your student card.

A lot of museums and other are free for all on the first Sunday of the month.

For all people under 26, Louvre is free on Friday from 18:00, start closing at 21:30.

On Monday, Orsay museum and Versailles castle are closed. Louvre museum is closed on Tuesday.