Rules
Robot Combat Rules
Rules around building and competing with robots are focused on keeping things fair and safe. Robots can be dangerous so be sure to take precautions when building and testing your creations.
Robot Combat rules typically cover both robot construction and match procedures. There is no single governing body for Robot Combat which means each event can use whatever rules they like but the different rule sets have a lot of overlap. The first thing you should do before building your robot is to figure out which event you are building for and determine which rule set they use. Before you get too far into your robot make sure to know if the event you are building for have any exceptions for changes to the standard rules. Also be aware that any event organizer may disqualify a robot if they feel something about it is unsafe so if you think you've found a loophole or workaround to make your bot more destructive, clear it with the event organizer before you show up.
Sparc.tools has the most commonly used rules for Robot Construction and Match Procedures.
The Fighting Robot Association is centered in the UK and most events in Europe use their rules. The RFA rules are very similar to the Sparc.tools rules but there are a few differences so if you plan on competing in events across the two rule sets be sure that your robot will qualify.
The Norwalk Havoc Robot League has their own set of rules and have some differences in weight allowances for multi-bots.
Battlebots is a TV show that features 250 pound fighting robots and they have their own rules. Many of their rules are similar to the other rule sets but they have an active weapon requirement and further limitations on weapons for safety reasons.
Judging Systems
More detail and references are needed.
There are several different judging systems. One used by many events is from Sparc.tools. Their system has judges assign a total of points based off of Aggression (5 points), Damage (6 points) and Control (6 points) between two opponents. With the odd number of points and three judges there won't be any ties.