We spent a month in Venice during the last Art Bienniale, and are going back this October. We did not feel the city was any more, or less, crowded because of the event--Venice is always crowded during high season, and the cruise ship passengers make it more so--but they are unlikely to attend the Bienniale.
There are two areas of the Bienniale, Giardini and Arsenale. A ticket is good for one full-day entry into each venue, and they need not be on consecutive days. you can read about ticket purchase here:
http://www.labiennale.org/en/art/tickets/index.html
There is a slight discount if you buy online, but you cannot get senior discounts that way so we went through the ticket line. It was just off Via Garibaldi if I remember, and there was basically no line.
The Giardini venue consists of a number of national pavilions (permanent buildings), each with an art installation representing that country's artists. Itis very eclectic, sometimes weird, sometimes beautiful, and often political. We spent quite a bit of time in the French, Spanish, British, Japanese, and US pavilions, and others which I do not recall. One film in the UK pavilion was absolutely amazing; We watched it several times there and then later online. I will see if I can find a link to it.
We returned another day for the Arsenale venue which was organized very differently. It is pretty amazing that they allow public access into this place and that was part of the experience. we enjoyed that more than the art.
We did not find either venue particularly crowded, but that was October.
People do not dress up in designer clothes to walk around the grounds and visit the pavilions. Just wear what is comfortable for a day in Venice ( and lots of walking). There are special events associated with Bienniale (music, theater, dance) and people probably dress up for those, but they are separate and expensive tickets. We did not go to those.
There are also some free venues scattered around town, and they are well worth visiting if you see one. They are for countries that want to create an exhibit but do not have a permanent pavilion. We found one just off a campo on our way to the Accademia Bridge, maybe Campo San Stefano or even Campo Manin, and decided to go in.. It was a small Asian Muslim country---maybe Uzbekistan? And it was truly amazing. The lower floor was carpeted with red woolen carpets on every surface ---anninteresting display of the local handcrafts. Upstairs there was a moving photographic exhibit of weddings, and then several rooms with very clever and innovative installations---metal sculptures that looked totally random but when lit from the right angle created beautiful shadows. Hard to describe, but we were captivated. my husband took lots of photos there.
On another day we found a friendly little temporary bar just off Via Garibaldi, sponsored by an African country, with a shaded courtyard, great music, and refreshing drinks. We were by far the oldest people there but were made very welcome.
Look around, keep your mind open to new things, and you will love it.