There are many different methods editors use to approach their work. One method, by Edward Dmytryk, who was a film director, created seven 'rules of cutting' that a good editor should follow to have a successful piece of work:
Rule 1. Never make a cut without a positive reason
Rule 2. When undecided about the exact frame to cut on, cut long rather than short
Rule 3. Whenever possible, cut in movement
Rule 4. The 'fresh' is preferable to the 'stale'
Rule 5. All scenes should begin and end with continuing action.
Rule 6. Cut for proper values rather than proper 'matches'
Rule 7. Substance first - then form.
I agree with the majority of these rules, but think it changes for the style of film you are trying to create. For example, I believe that a drama should move on an emotional state rather than movement because I believe it would have a bigger impact on the audience, whereas for an action scene, I feel it would be more appropriate for me as an editor to cut on movement and action to make the film dynamic and also ensure that it keeps the attention of the audience at every turn.
I like that a cut shouldn't be made without a positive reason, because you need to have confidence in your edit, and if you aren't sure why you're including or aren't too happy about the choice of cut, then I believe it shouldn't be there. The edit needs to be precise and needs to flow together to create the final work, therefore every cut made needs to fit with the others in a sense of standard as well as (sometimes) style and structure.
I also believe that starting an edit with a 'fresh' outlook is important too. Throughout other projects I've noticed that approaching footage only at the stage of post-production inspired me with narrative structure ideas, style as well as noticing errors made within the production that the production and pre-production teams missed - when you're engrossed in your role, you sometimes overlook little things, whereas I'm only being shown the footage so I have a brand new outlook on the finished product. The idea of cutting fresh could also mean not working in a 'cliche' style of editing for a particular film. Using conventions of editing is good, because you want your edit to be 'invisible', but use the edit to shock the audience and entice them to carry n watching the piece.
Overall, I think these methods are very important to my way of editing, it also shows me what best captures the audience and how to work efficiently with my footage.