There will be caucuses held on Saturday, February 9th, at 1 PM, at various precinct locations depending on party. There will also be a primary election on Tuesday, February 19th, all day long, at the usual polling places.
Here's the trick: For the Republicans, the primary and caucus each count roughly one-half for allocating the delegation from Washington state. For Democrats, though, the state-mandated primary is held but its results are ignored: all delegates are allocated via the caucus. The Democratic presidential primary is just a straw poll in Washington state.
To participate in the caucus on Saturday, you must show up to your precinct's caucus location at 1 PM. Caucus locations are set by the legislative district party organizations - their websites should have details. Important: your caucus location may not be your normal polling place! In fact, it likely isn't.
The caucus is essentially a meeting of party members, though depending on party rules you may or may not need to be registered as a member of the party to participate. The Democratic requirement is just that you consider yourself to be a Democrat and that you swear not to participate in another party's nomination process - no registration is required.
At the caucus, you'll sign up or group together according to the candidate you wish to support. A count is done, and then those groups without enough voters to earn a precinct delegate will be given an opportunity to join other viable groups. After this final count, each candidate group has earned a certain number of precinct delegates, who will go on to participate in a similar process at the legislative district and state levels. The delegates to represent the precinct are then chosen from each group according to the numbers permitted.
Of course, this all means that we'll only have an estimate of delegates won by each candidate when the caucuses are over - the actual numbers won't be strictly decided until the state convention, which I think is in April.
If anyone's curious about my own preferences, I'll be happy to elaborate. I'm also happy to help people find their caucus locations. (They're determined by precinct, which is the 4-digit number following your legislative district on your voter registration card.)