The year's-best volumes reprint stories that were published the previous year. Therefore, writers can't submit material to them that hasn't already been published. In general, it's more efficient for magazine and anthology editors to send copies of their work to the year's-best editors than for writers to individually send copies of their work.
(In some cases, such as the Nebula volume, the year's-bests are not open to submissions of any kind.)
Most year's-best editors have to make their final decisions for the next year's volume before the end of the current year, sometimes as early as mid-October. Therefore, if you're an editor of a venue that's published speculative fiction in the current year, you should send that material to appropriate YB editors for consideration in the following year's volume. If it's October and you're planning to publish more material before the end of the year, you should send advance copies or galleys to the appropriate year's-best editors.
If you're a writer whose work has been published in the current year, you may want to check with your editor to make sure that they're sending copies of the work they published this year to the appropriate YB editors.
This site may eventually contact contact information for the various YB editors, but it doesn't yet. For now, follow the guidelines links (where available) for contact information for those editors.