Just for one day (24h) and travelling only inside Paris I like to use a Mobilis ticket. You can use it for unlimited travel with metro, RER, bus and tram, with a few exceptions like going to the airports. Price depends the Zones you want to move around, cheapest dayticket is €7. You can hoho and change mode of transport as much as you like without the concern buying another ticket.
Read also: http://parisbytrain.com/paris-metro/#mobilis The site mentions only the metro, the company running public transport in Paris, RATP mentions the other modes of transport too.
You can buy at the ticket booth, but also at the automatic ticket dispenser. Larger stations has employees who can help with using the menu as the Mobilis option is a bit hidden away in the menu.
There are more “ticket options” like Paris Visite with more possibilities, but more expensive.
Keep indeed the ticket with you till the last exit, not only for being checked, but in case it is a RER station you can only exit through automatic gates and open only with your ticket.