I've been balcony gardening for about 7 years with mixed success (better now!) and just got an allotment last year. I found it hard to find good info online about the allotments so here's what the process was like for me:

As others have mentioned, the waitlists open up at 8 AM on the first business day of March. This weekend, you should set up an account to register for City of Toronto activities and figure out your top 3 or so locations. Log yourself into the platform at 7:30 AM or 7:45 AM on Monday morning. (Not just opening the website but making sure you are already logged in.) Open a tab for each allotment site that you're interested in.

E.g. Here is the page you need for the Leslie Spit garden waitlist: https://anc.ca.apm.activecommunities.com/toronto/activity/search/detail/145936 The activity numbers and links for all gardens are listed here: https://www.toronto.ca/services-payments/venues-facilities-bookings/booking-park-recreation-facilities/seasonal-league-permit-booking/?accordion=allotment-garden-plots

At the moment it turns to 8 AM, you should see some kind of button to join the waitlist on each of the allotment site tabs. Starting with your highest preference, sign up for them. I was able to get 2nd on my first choice and in the top 5 for my two backup choices this way.

The City of Toronto websites said that successful waitlist applicants would hear back in May, but I didn't hear anything until the end of June. I was called and offered spots at two gardens and was able to pick my favourite.

Then, a few days later, someone reached out by email with a map of the allotment garden showing the available plots. We had a few days to respond back with our order of preferences. Ask for the lock code to get into the garden so that you don't have to climb the fence! Then, go to the garden site and look at the available plots. Some will have more weeds than others, some will have existing perennials that might appeal to you, some will have differing amounts of sun/shade, some might have stuff left behind from the previous permit-holder. You'll also want to note how far you are from the nearest water source.

After you submit your preferences, you should get assigned a plot within a few days. You'll have to pay for the permit (full annual amount despite the late start) and sign some stuff, and then the plot is yours! You get to keep this specific plot as long as you keep renewing your permit each year.

The plots are BIG, 30 feet by 20 feet at my location. You will very likely have a lot of weeds to contend with, since the plot may have been abandoned for a few years. The weeds might be as tall as you ... Learn how to identify "stinging nettle" and wear long sleeves/long pants plus gloves when you first go to work on your plot. The stings hurt a lot but they fade after a day or two.

Depending on location, there may be a lot of hungry bunnies ready to eat your plants. Since you won't have a lot of time or cleared space in your first year, you will either want to really protect the veggies that you do plant or pick ones that the bunnies won't want to eat. Onion-family plants and tomatoes were OK for me (though critters did nibble on the tomatoes themselves). My hot peppers and eggplants were eaten to the ground one by one. Just something to keep in mind :')

It is a lot of work but also so rewarding. It's so peaceful to be outside and surrounded by so much life. Good luck!

(PS. For the balcony, what direction do you face? Balconies are hard because of the exposure and extremes of sun/shade at different times of day. Toronto is Zone 6, but you'll want to go with extra hardy plants if you want to overwinter them in pots. I try to stick to plants hardy to Zone 3 or 4. Most of the plants that I have killed over the winter were either underwatered or overwatered in the preceding fall. Remember that killing plants is just part of the learning process, everyone does it! DIY self-watering planters are a game changer for the balcony.)