Most of the major tourist attractions in Washington DC are free. The parking probably won't be.
As with so many major cities in the United States, parking in Washington DC is easy to find in the outlying suburbs and satellite communities, but much more difficult to find in close proximity to where you want to be. Because of the high numbers of commuters as well as tourists unfamiliar with rush hour traffic designations, driving anywhere inside the beltway is extremely slow during traditional commute hours. However, commuting drivers will often have some type of designated garage parking, usually on a monthly pass basis. The tourist is not so lucky.
Free and metered curbside parking is available but hotly contested. Inside the beltway, consider yourself fortunate if you find a space in less than an hour during regular business hours. For metered parking, you will need coins. Handicapped persons will need a permit from the city: a out-of-state licence sticker or dashboard sign is not adequate. Many streets which offer free parking during the day are designated no-parking during rush hour. Time limits and no-park zones are strictly enforced and towing is common, so check the signage carefully if you don't want to find yourself on an inadvertent tour of the local impound lots.
In a practice unique to Washington DC, the Secret Service may move your car if it happens to be near the President's path. In this case, they will leave it on a nearby street, but it is entirely up to you to find it.
You can find privately owned parking garages in every part of Washington DC. If you have an Internet-capable cellphone, Washington DC Parking Rates shows a comprehensive selection of private parking within blocks of your intended destination, including rates and hours of service. (When searching for an address, remember to reference the city quadrant first.) Parking costs are generally calculated by the hour or by the day, or if you are staying for an extended period many garages offer a monthly parking pass. Unless you come from a major city, you will find the rates very high.
It is much easier to find central district parking during weekends and minor holidays. As well, the rates will usually be cheaper.
Your best bet is to invest in a SmarTrip card, park at one of the outlying Metrorail parking lots and take the metro in. Parking in these lots rarely runs over $5 per day, and weekend parking is usually free. The current base cost of the card is $5, with a minimum additional fare value of $5. You can buy and load SmarTrip cards at any Metrorail station with a parking lot, or you can order them in advance of your visit from the Washington Metropolitan Area Transit Authority website.