The average time one spends in the Basilica’s waiting line is about 45 minutes.
Before getting in line - go to the Ateneo San Basso (right around the corner) to check in your bag. You will be sent there anyway if you have anything bigger than a purse with you. When your bag is checked - you’ll be given a plastic tab that can be used to bypass the queue at the front.
You can skip the line by booking your ticket. The fee is € 2 (while the entrance to the Basilica is free). Choose the date and time slot for your entrance here. You’ll be able to skip the whole line and enter through a different entrance (Porta S.Pietra). Booking is available from April to November and can be done up to 10 minutes before the visit. The only problem is that you’ll need to have the ticket printed.
If you don’t want to spend money on the booking - come to the Basilica at the opening time or just after. That’s when the waiting line is the smallest. You can also try to come in the evening, an hour before closing time, when there are no more group visits. Try to avoid midday (especially in high season): though the gilded mosaics look most impressive at this time, this is the most crowded period of the day.
Another option, is to join a group tour, that will also allow you to skip the line!
The busiest months in Venice are April, May, September and October.
Avoid weekends and religious holidays. On religious holidays the Basilica is closed until 14:00.
During low season (especially December-January) the waiting line is small, so it’s better to come from 11:30 to 12:30 when there’s enough light to admire the mosaics at their very best.
Tips for a few days in Venice
This page will give you many tips to avoid crowds in Venice as well as crowd schedules for top tourist attractions in order to plan your visits.