There are plenty of coin-operated laundries around Paris. You can find them on the yellow pages. There's always one within walking distance. Laverie is a laundry (most if not all are unmanned these days), pressing is a place where someone washes your clothes for you (mostly for things that require special handling).
Laundries are primarily coin-operated. Many but not all accept banknotes and give change. Few if any accept cards.
Typical prices are around 3–5€ for a small load, ~10€ for a 15kg load (but you surely won't have 15kg of clothes to wash all at once for a single person!), ~1€ for a run of the dryer. You can typically buy detergent as well but if you're staying around for a while buying your own from a supermarket is cheaper.
Typical opening times are something like 7–22. Often the washing machines won't start after a certain time which could be as early as 19:00 or thereabouts (it depends how good the noise insulation is and how much the neighbors complain), so if you plan to go in the evening, do make sure to check the times (“dernier lavage” means “last wash”, i.e. you must start the washing machine before that time).
Usage should be fairly simple: put your clothes and detergent in a machine, select the program, go to the payment machine, type the number of your washer/dryer and pay, then wait until done. Many but not all places have signs in English.
Don't expect dryers to leave your clothes completely dry. Use the dryers to get most of the humidity out (or don't use them in summer) and hang your clothes at home overnight to finish drying.
Parisian laundries are typically very bare-bones affairs: just the machines and a couple of chairs. If you want a drink while waiting, go to a nearby café. A few places do have wifi.