Don't give points. Start with maximum score. Take away a point for each observed error. Note that 'a point' may be measured in whole numbers or or percentages of numbers, which you'll be told before the tournament starts. For example "This group of competitors will be graded from 3.50 to 4.00." Then you'd take off .1 for each error, something along those lines.
In a closed tournament, I am looking for errors in the kata based on what the parameters are for each kata - which I should be aware of as a yudansha. If it is an open tournament, it's more difficult, since the competitors may be performing a kata or form I am not familiar with. However, some things are commonly seen as errors, such as an excessive pause (usually accompanied by a panicked look) indicating the competitor has forgotten or is unsure what to do next, or not ending up facing the direction they started, or 'sloppy' movements (depending on belt level and age), and so on. Crispness, balance, speed (with clean moves), power, flow, confidence, these always tend to show through.
I was worried the first few times I was asked to judge, but soon realized that my scores were within fractions of the scores other judges were giving on the same competitor, so I was apparently seeing the same things they were. So it was all good.
Best of luck!
Trust me, judging kumite is tougher.