it isn't the best situation but isn't a bad one either, there are books that explain how write (a book, a script...) but i don't know any in english and probably you don't have the time for it, now it's better if you use your own criteria, anyone can make a critique (is the correct word?), only try to be just and don't fall in personals preferences, if you make a "subjective critique" and no a professional one, i don't believe anyone will get mad.

Heh, didn't you know the best intentions pave the way to hell?

Jokes aside, ^83-127's advice is good, do your best to be fair. Being a competition judge is more about giving everyone the same equal chance and making your choice on who you believe has done the best than giving critique. That said you may need to justify why you pick whichever story you do. You will inevitably have some personal preference, don't worry that is normal. You just need to remember that just because we don't like something does not mean it is bad. For example I don't like the Harry Potter series, but I still believe and would argue that it is exceptionally well written.

If you do want to read about something on writing I would highly suggest the book On Writing and World Building  by Timothy Hickson, or you could watch his Youtube channel Hello Future Me. The book compiles his work into on easy to read place. Something with shorter videos would be Terrible Writing Advice which is run by another author that make short funny videos about writing concepts. If you do have any specific questions feel free to ask.

By the way a "subjective critique" would lean towards personal preference, the correct term is "impartial."

As for critique, look for both what is done well and done poorly, it isn't critique if it amounts to nothing but pointing out someone's failings. If you have to offer someone direct critique use both, not just one or the other. 

To be completely honest the critique writings and essays I am able do is because of the shear volume of material I have read. I can't give you that experience, you are going to have to rely on your own experiences, knowledge, and training, but I do think you have a solid base to work with.

What is the Genre by the way? Also, do you know how the scoring will work for the contest?

thanks 83, kev that really helped. (except the hell part -_- )                                                                   also hey there is a new moderator!!! WOW! hope to get along with you rigel-san :3

well at first it was to be a 3 chap modern fantasy (as like elves walking in the streets or something like that) but then admin said we should get to a genre with voting. dunno how the scoring will be...

there are about 6 writers who will absolutely participate and maybe about ~20 chibis (the role name admin given to the regulars) and they can participate too. 

in the feedbacks i used to give them i usually made points on what part i liked and which parts i would like to be different, then the author usually asked me some extra questions on some parts to get the feeling and reation of a reader on that certain parts

"You just need to remember that just because we don't like something does not mean it is bad" lol well on that part just recently i got into a discussion with some guy to say classroom of the elite is no good (i dont like it XD) and eventhough i was screaming from the begining to the end that its all "a fun chat" "weeb chat" "dont take it serious" still he was pissed and in the end blamed me for wasting his time in a prank chat. which equally pissed me off because he was blaming me while all he had to do to end the argument and tend to his "important jobs" was to click close on the screen. yeah i guess that argument tainted my reputation a bit as a troublemaker or troll...

Character delevopment, accuracy in setting, writing style, writing ability, story and characters not created to convey a moral message. Instead if any moral values are conveyed have it seem like a natural effect of the plot and not make it seem like the characters were solely created for that purpose, but instead have natural personalites and never have the character's do things in the story that contradict their personalities just for the sake of plot. That's what I care about most as a reader and how I judge books anyway.

^Good advice... after doing all the "Pro" stuff that other people already told you here before, just ask yourself... Did I enjoy reading it? Is it good? Is it to my taste? What message is the Author trying to convey?

Check few stuff:

Theme.

Consistency.

Genre.

Feelings transmited through writing.

Check if the readers will care about the characters, not only the MC or MH.

The Start> Middle> End > Conclusion.

I could write more, but I don't know how to express it in English ?

Good Luck!