My homebrews come in three "flavors" (not all of which have been posted yet):

1. Fixes. These are meant to solve a particular mechanical or gameplay problem (e.g. an unbalanced tier system) with a relatively low amount of change. My approach to that is to try to identify the essential underlying problem (e.g. is it a scaling issue, an overall over/underpowered feature or class, abilities that work against each other when they should work with each other, etc.)
2. Homebrews. These are meant to give a particular flavor to the campaigns in which they are used (unlike fixes, they are not meant to be used in all campaigns). My approach to that is a very stylistic-based one; I start with the concept, and try to make mechanics to fit the intended fluff.
3. Remixes. These are similar to fixes, but are meant to "fix" a poor (or not-as-good-as-it-could-be) match between the fluff (or occasionally a new, IMO better, fluff for the same class) and the mechanics, and involve far larger changes (frequently up to the point of being practically a different system). My approach to that is largely stylistic-based as homebrews are, but is meant to replace the existing rules rather than create another option as homebrews do, and is meant to be far less campaign-specific (although it's still not meant to be used for all games like fixes are.)