Everything I say below is subject to change, of course.
When: Open 10-6 every day except Mondays from mid-April to mid-November in odd years even years. Alternates with Biennale Architecture.
Update: The 59th Biennale was rescheduled from 2021 to 2022, running from 23 April 2022 to 27 November 2022. The 60th Biennale ran from April to 24 November, 2024.
Where: Exhibits are split between the Arsenale, an old military post, and the Giardini, a park. They are near each other, and at the opposite end of town from the tourist-heavy train station and cruise ships. There are also country-sponsored pavilions on these sites and scattered in town.
How much time: 3-4 days for the Arsenale and Giardini, a few more days for the exhibits in town.
Tickets: The Arsenale and the Giardini take different tickets. None of the country pavilions outside the grounds of the Arsenale and Giardini asked me for a ticket. Single-entry tickets are available online but why would you? The more useful is the multi-day, multi-entry pass. I paid € 35 for a 3 day pass. This pass must be bought in person and with ID because the ticket is associated to you. I suggest you go with your passport to the Arsenale ticket office the afternoon before your first visit, to purchase a multi-day pass. And while at the ticket desk you might want to pick up the very nice guide; it's around € 20.
Photography is expected.
Vaporetto: The Arsenale and Giardini each have their own stop but they're not far apart. Both are an easy walk from San Marco, though I sort of avoid that busy piazza.