How do You review games-

 
So i review games by looking at what i really enjoyed in the game ususally mentioning that in the opening of my review.
Then i go over story elements i liked.
Then i talk about the gameplay in the game.
Then i look at both Graphics and sound design.
Before finishing up with more things i liked in the game.
 
Most of my reviews are generally positive as i find it difficult to write bad reviews as -

• Im generally a very nice person and being a harsh critic isnt in my nature
• I dont BUY bad games, but if im psyched for a game and it fails, then it will have a bad review.

Pretty much the same way as you're doing it.  
Only difference is that I'll give harsh critic if it's needed and I don't care about the fanboys reaction to said review. 
And by the time they read it, it's too late to pull it since when they read it it's already printed.  
 
And there's no scores either, it's either Buy, Rent or Forget about it fast

I take notes, develop an opinion, and organize that all in writing.

with 5 wheels of cheese and 2 cases of booze

"  

• Im generally a very nice person and being a harsh critic isnt in my nature
•  "

I used to take several notes as I played the game, but that kind of sucks from a fun perspective. I don't review in a traditional manner anymore. I just go off memory now, maybe looking something up if I really need to. If I don't remember it, then it probably isn't worth mentioning. I also don't like to call them reviews though. More like, "my thoughts on the game" =D

I keep it short.  I figure if someone was looking at a random user review they just want a quick opinion.

I finish the game, and then much like Caesar, I give the game a thumbs up or a thumbs down.

i don't really. i can tell you what i liked or didn't like about them if you ask, but i don't write formal reviews usually.

" I take notes, develop an opinion, and organize that all in writing. "

With my penis.  If I get hard and stay hard. it's a good game.  If I get hard and go soft, it's middling and if I can't get hard at all, it's Borderlands.

Magick.

I like to start out by soliciting bribes from game companies. The better I'm rewarded, the more favorably I'll write the review. Other factors come into play, of course. For instance, has the company given me bribes in the past, or early and free access to their games? Is the game heavily promoted with it's own beverage of some form? I don't care if it's Mountain Dew or slurpees, that kind of publicity will raise any game's score by at least 10%. Oh, and if I'm given free samples of this beverage, I'll throw in a really supportive video review as well. Another big thing these days is exclusive preorder-only content. If it a game has that, it's clearly a great product. Sure, I won't get it since I'm getting the game for free without the pretty box art, but I can admire what they're doing, because it's just so right. Oh, and if the game lets me boost my gamer score with minimal effort, that's just fantastic. I'll be so happy about it that clearly my joy will be reflected all over the review.  
 
Okay, I'm really letting this get out of hand, so I'm gonna stop before people take it too seriously. Anyway, uhh... I look at a number of factors, and generally I don't review many games anyway. When I do, it's often quite a while after the game's release since I let it mull over in my head for a few months and compare it to what else is out there. Sure, people say you can't compare certain games because it's like apples and oranges, but I don't mean a straight contrast. Just the level of quality. The level of innovation. If the game pushes the envelope in any way. Really, though, I'm just going to cut my rambling short here, because what matters most, by and large, is the gameplay. How well it plays, how it controls, how fun it is to play, how much you'd like to keep playing it. I don't care what anyone says, there is no single aspect more important to a game than gameplay. You got people that claim story is most important, but they're flat-out wrong. Story can help engage a connection between you and the characters, and that can certainly alter your feelings for the game, but as we all know, games can do perfectly fine without them. Ever play a game with a really great interesting story and boring, dull gameplay? Yeah, it kind of sucked to drag yourself through it for the story's sake, huh? Exactly. So gameplay first and foremost, and the other elements should be taken into consideration as well. The style, the graphics, the music, the sounds, the characters, the story, the way the game impacts you as the player, how well everything ties together, etc.  When I write review for games, I must have played it thoroughly. Preferrably to the end and further, trying out everything it has to offer. 
 
As for the order, I usually start by giving a brief synopsis of the game. Just trying to give a little insight into what I know about the history of the game that I feel is important. It just serves as an introduction, then I'll probably begin to tackle the setting and atmosphere before diving into the gameplay. I think it's good to have some structure and not just throw everything into the mix all at once. The way that it's ordered could be altered by the quality or significance of that particular aspect in that particular game, but generally I'd probably go with an introduction, then the gameplay, the opening story (with no spoilers whatsoever, in fact I keep this as brief as possible because I like to go into games and movies as open-mindedly as I can), then the graphics and sound, followed by any other tidbits that I think are worth noting. Oh man, walls of text again. I'm sorry. This site needs a TheGreatGuero-Wall-of-Text filter.

I've drastically simplified my reviewing style over the years. I now write one or two line reviews and use a 4 star system. The ratings are: Didn't like it, Liked some of it, Liked most of it and Loved it. The rating is purely based on how much enjoyment I derived from the game by the end of it. I mentally skim through the game recalling what was enjoyable and what wasn't and pick the rating that feels appropriate. I don't "judge" the game based on it's graphics, sound, replayability or anything like that unless they've severely impacted my enjoyment of the game.

Example:

Batman: Arkham Asylum[ 11/14/2009 ]
(Fantastic! Fun and engaging the whole way through except for Riddle cleanup.)
 
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That's it. I don't care to say any more about it. It's worth playing and I loved it. You can watch a gameplay video to see what kind of game it is or read a preview or some other game material to find out how many levels their are or what the plot synopsis is. :)

I review in categories starting with gameplay, then graphics, sound (only if needed), and then re-playability. I do not use scores or quick references as I hate being distracted with scores so I don't use them myself.

I don't. I read other peoples hard work but then don't listen to what it says. No matter what someones personal opinion will shine through in a review and if they hate the genre/series/etc then it will show and will be bias.

Introduction
story
gameplay
technical (sound, graphics and art)
achivements/trophies
conclusion
 
and sometimes a rating, I don't like rating systems

I play the game, without thinking about it in the context of a review at all. Then, when I feel like it, I start writing the review. I think back, and assess the game purely on what I remember from it. Then, I talk about all aspects of a game in a pretty specific order, because knowing what I'll talk about in what order makes it easier for me to structure my review and avoid forgetting anything major.
 
The order goes like this:

1. A small intro that basically says in one or two sentences which demographic would enjoy this game, and for which reasons.
2. After that, I explain the premise of the story.
3. Then, I dedicate some lines or a new paragraph to judging the story.
4. I then move on to gameplay. I spend a number of paragraphs talking about various gameplay aspects, such as controls, mechanics, etc.
5. After the gameplay, I tend to work on presentation.
6. Finally, my finishing paragraph basically sums up my feelings on the game, and whether or not I'd recommend buying or renting it.