This map shows when the primary elections and caucuses will be held in the 50 states and D.C. Not shown are the elections in American Samoa, Guam, Puerto Rico, the Northern Mariannas, and the U.S. Virgin islands. Also not shown are Democrats Abroad. All of these also get to send delegates to the Democratic National Convention. The total number of delegates who may vote on the first ballot is expected to be 3,769. If no candidate receives a majority on the first ballot, on the second and subsequent ballots, and additional 766 superdelegates get to vote. These include all members of the DNC, all Democrats in Congress, all Democratic governors, and a few distinguished Democrats such as former Democratic presidents.
All 50 states choose delegates by district, usually congressional district but in a few cases by state senate district or by county. District delegates are allocated proportionally among the candidates who got 15% or more. So for example, if candidates A, B, and C got 25%, 20%, and 15%, respectively in some district with none of the others making 15%, A, B, and C would get 25/60 (41.7%), 20/60 (33.3%), and 15/60 (25.0%), respectively, of the district's delegates. There are complicated rules about rounding but generally fractional delegates are rounded to the nearest integer. This can have unexpected effects. For example, consider a district with four delegates and two candidates who made the 15% cut, one with 60% of the qualifying vote and one with 40%. They get 2.4 and 1.6 delegates, respectively. After rounding, they each get two delegates. That means that the landslide victory of the first candidate doesn't result in any net delegates over the loser. For more information about the details, see The Green Papers.
In addition to the district delegates, each state gets at-large delegates determined by the statewide vote, sometimes in complicated ways involving both the popular vote and the state convention. Again there is a threshold of 15% below which a candidate gets zero delegates. The sum of the district delegates and the statewide delegates is how many voting delegates the state has on the first ballot.
When you mouse over a state, the pop-up box has something like (272 + 144 = 416 delegates). This means that 272 delegates are elected by district and 144 are elected statewide, for a total of 416 delegates.