All eyes will be on wrestling the next few days, unlike archery/shooting/boxing/hockey/weightlifting/javelin, many people don't know much about wrestling including how points are scored, how winners are declared etc. Maybe this will make it easier to follow.
There are 2 kinds of wrestling events in Olympics, Greco-Roman and Freestyle.
Greco-Roman (GR)=Upper Body, nothing doing below the waist
Freestyle=Whole body comes into picture
Men have both these disciplines, further divided into weight categories. Women have only Freestyle variant.
Indians traditionally don't do well in GR, historically USSR/Russia, Eastern European countries have dominated this sport. Other wrestling powerhouses too have won medals but when you think GR you think Russian (or Soviet) Bear.
Freestyle is India's strength, all our Olympic medals in wrestling have come from this variant. From KD Jadhav in Helsinki to Sakshi in Rio. All our wrestlers in Rio are from Freestyle portion, none of our GR wrestlers qualified. Many countries come into the picture in Freestyle: Russia, USA, Japan, Iran, Turkey, India, China, Canada, Cuba, Mongolia, Georgia, Azerbaijan, Central Asian 'stans', Eastern Europe, Scandinavian countries etc.
There are other variants like Folkstyle (USA, many matches/content on YouTube, somewhat similar to Freestyle in terms of skills required), Kushti (India), Sumo (Japan), Sambo (Russia, limited striking allowed), Bokh (Mongolia) etc. None of them in Olympics but you can watch Folkstyle videos to get more insights on techniques used in Freestyle.
From Olympics pov only GR and Freestyle are important. Both involve takedowns, pins, tech falls, turns, escapes, reversal etc. but vastly different (both disciplines highly specialized), even points scoring is different.
Below (two) videos give brief summary, how points are awarded, how to pin, basic rules etc.....just 5 minutes long each. Watch the Freestyle video, GR is optional since most of us will skip matches not involving India. Still to appreciate the sport you can watch both. Some minor differences in actual Olympics (rules keep changing including how many pts to award, nothing major) but they give nice overview. Maybe watch a couple of live matches after this to get a better understanding, that way you can enjoy matches of Indian wrestlers (in action the next few days), 2-3 medal prospects as well. We have 2 bronze medals in wrestling, repechage rule explained HERE
They wear a funny kind of clothing (both men and women), called singlet, skin-tight ones that too. This is done because loose clothing is extremely dangerous in the sport, if a wrestler's hand gets stuck in some loose T-shirt or shorts good chance of breaking fingers or worse, dismemberment of fingers....because of the forces involved. Even when wrestlers train in shorts they ensure that pockets are cut out, for precisely the same reason, still risks will be there. In ancient Greece they used to wrestle naked, in kushti almost completely naked. Singlet is the only viable alternative.
Brutal sport this, broken bones (sometimes jutting out of the skin!!!!), ACL tears, head/neck/spinal injuries are par for course....also physically the toughest sport since unlike boxing, whole body is involved in the tussle against a similarly built athlete, and always in contact. Oldest sport known to mankind as well, finds mention in all civilizations and cultures, at least wrestling in some form.