According to NHL rules, the first buyout window opens on the later of June 15th or 48 hours after the Stanley Cup final and closes on June 30th at 5pm EST.
The exact rules for contract buy-outs can get a bit murky. General Fanager has a concise breakdown of all of the rules regarding buy-outs. However, to simplify, the team has to notify the player in question and place them on unconditional waivers. Once the player has been notified and has cleared waivers, the player has been bought out.
A buyout is paid over twice the number of years remaining on the player’s contract, at a rate of one-third of the total salary remaining for players under 26, and at a rate of two-thirds of the total salary remaining for players 26 and older. A buyout calculator is provided by Spotrac.
The Cap Hit
The resultant cap-hit is even more of a convoluted formula. The fine folks at CapFriendly do a decent job defining how buy-outs affect a team who executes a contract buy-out.
It is highly unlikely that the Capitals buyout any existing contracts, however the Capitals may find interest in a player that is bought out and released from their existing teams.