Cards and passes can be bought at any subway station (look for the ‘casa de bilete’ booth) or at the orange ticket machines placed in most stations: there are two and ten ride tickets, day, week and month passes. A one month pass is a good idea if you are planning to travel a lot. Cards must be validated upon entering the station at the machines there. As of end 2019, contactless payment for the ride has been implemented, and you can pay directly with the credit card upon entering any station. Combined STB (surface transport) - Metrorex (subway transport) cards also exist. Find more details on tickets and lines on the English page of Metrorex.
Built under the former Communist regime, master of the super-planned economy, the lines do not cover the city well; whole districts like Drumul Taberei, Pantelimon or Ferentari are not served by it. They are currently expanding the network, with the OTP airport line and a West - East line crossing the centre and then proceeding to Pantelimon District in the planning, but that is a slow process. The latest addition was the Eroilor - Drumul Taberei line opened in 2020. For the time being, to get to Bucharest OTP, your best bet is to get by subway to Piața Victoriei 2 and get bus #783, #784 or to Gara de Nord and take bus #780 or to Băneasa Shopping Centre and take bus #782 (special tickets apply in these cases, see here). Alternatively, from Gara de Nord there is a train service to within 900 m. of the airport, distance covered with a van included in the train fare (the airport rail connection and terminal station will be opened towards the end of 2020, when the van service will be unnecessary). You can buy the train ticket at any ticket office at the station or, if you are in a hurry, from the conductor on the train (the same tariff applies). Read my Getting to Bucharest by Air post for more data on this service.
A few years ago, as the original trains were getting old, there were signs of improvement when the company running them, Metrorex, decided to buy new Bombardier (made in Sweden and put together in Craiova) and later complete their stock with CAF (made in Spain) trains. Oddly, every new train features a bodyguard, occupying space (sitting, chatting) and supposedly 'defending public order', as the official line goes; well, actually the IDs the guards bear mentions "pază tren" (En. train security); meanwhile, most of them are of the overweight, old, tired and helpless kind. Oh dear.
Access for persons with reduced mobility. The subway does not provide a homogenous rule: most of the stations have dedicated facilities to get to the surface (elevators, often with a change at the access gates where wide, double way gates are provided), while others, including some quite busy ones (e.g. Obor, Tineretului), do not generally due to the technical local situation; a map showing stations with such facilities can be found here, but mark the fact that - where they do exist - such elevators are located at only one end of the platform, quite often not by the busiest exit. For those in crutches or with a less severe walking problem, most of the station exits have escalators, even though sometimes not all the way to the surface. For more information on accessibility for those with reduced mobility in Bucharest, refer to my dedicated article on the matter.