If your visit to Tokyo is during the period the Grand Sumo Tournament is held (mid January, mid May and mid September) the you should certainly not miss the opportunity to see this in person.
Popularity of the tickets have soared in the last few years, partly fueled by the rise in international visitors. Thus it is becoming extremely difficult to get tickets without paying a hefty charge to a middlemen.
About 300 non-reserved seats (the last row of the arena) do go on sale each day on a first-come basis. Usually you have to show up at the Kokugikan Arena by 7 am, sometimes even earlier. Only one ticket is sold for every person that shows up, in other words one person can't buy four tickets for the family.
When: Normally the tournament starts on the second Sunday and goes on for 15 consecutive days, thus ending again on a Sunday.
What time: The wrestlers in the lower categories start before 9 am, however the top-ranked wrestlers start to appear around 4 pm. This is when a majority of the crowd shows up, though you're free to arrive at any time of the day. The final match featuring the Yokozuna (highest-ranked wrestler) finishes shortly before 6 pm.
During the final 15th day of the tournament, the final match is over around 5:30 pm, with the awards ceremony following that.
Other chances to see Sumo
1) Seeing Dohyo Matsuri
The Dohyo Matsuri a Shinto ritual that is done the day before the Grand Sumo Tournament starts.
Open to the public for free, the gates open around 9:45 and the ceremony starts at 10 am. This is a ceremony to purify the ring and wishing for the tournament to be carried out safely without injuries.
There are no matches held this day, but all of the wrestlers in the top category attend this event, so this is a chance to see the wrestlers up close.
2) Going to a Jungyo - regional exhibitions
There are numerous Jungyos, which can be translated either as a regional or exhibition tournament held on April, August and October, a period in between the main tournaments.
While most Jungyos are held in rural communities, a few are held in central Tokyo as well. For example, in August 2017, there are plans to hold a Jungyo at Aoyama Gakuin University (8 Aug), in the Odaiba district (23 and 24th Aug) and at the Kitte Shopping Mall near the Tokyo Station (27 Aug).
The program will feature a comical explanation of the rules, chance to see the wrestlers getting their distinctive hairstyle done, and small kids challenging the wrestlers. There are also head to head battles of the top ranked wrestlers towards the end of the program, usually happening around 3 pm. The results in the exhibition don't really mean anything for the wrestlers so the atmosphere is much more relaxed in comparison with the actual tournaments (Imagine a friendly match in soccer).
3) Additional Events hosted by TV Networks
On February, Fuji TV and the national televsion network NHK host a one-day tournament at the Ryogoku Kokugikan Arena.
The Fuji TV event is held on the first or second Sunday while the NHK event is always held on the 11th as a charity event.
Both events feature programs similar to those seen in Jungyos.