If you are in the US and are interested in the Tokyo 2020 games, ticket requests through Cosport are officially open until May 31. You will need to be registered with the site in order to submit a request. Cosport is the only authorized seller of Olympic Games tickets in the US.
You will be able to submit as many requests as you would like (within reason), but nothing is guaranteed until you officially receive a confirmation e-mail that your requests have been approved. Tickets are available to be requested by different price categories: A, B and C.
A tickets will be closest to the front, B the middle and C the higher rows. According to the Cosport website, if the event has general admission that will be indicated in the request form. The only catch is the ticket prices have not yet been released. I believe they will have their pricing list out by the end of the week.
Some events will be understandably more popular than others and have strict limits on the amount of tickets per party per event that can be requested. You will need to look at the official event calendar to see where the event venues are being held and times. The Cosport website recommends you allow at least 2 hours between events if you are moving from the Tokyo Bay Area to the Heritage area. Expect lots of security checks and traffic.
You will be notified if you tickets requests have been successfully picked! You have nothing to lose by submitting for all your dream events. Once the tickets are confirmed you will have 5 days to pay for them. Ticket requests can be changed up until May 31. Note that there is no benefit of submitting your requests early. All will be given the same consideration. I wouldn’t recommend booking any accommodations or flights until you know for certain you have tickets to the games!