There are some general principles for designing good and intuitive levels for any kind of game (like push pull, adding landmarks, using Gestalt principles), but these are very generic by nature.
Mostly, I design my levels around the game mechanics. For every level I have a vision, a certain idea or interaction that I want to explore. For instance: there are enemies that chase the player as long as they can see the player. Then I create a (stealth) level where the player has to lure the enemies to different corners of the level in order to escape unseen. That's just one simple example - if your game mechanics and interactions are interesting enough, you can come up with dozens of such ideas. I start on paper drawing a general structure (for instance: the enemies start in these corners, and the obstacles are distributed like this, so this is the general path that the player should traverse...).
Then I create a greybox, for playtesting. For this it's important to be aware of all the details in your mechanics. For instance: in a platformer, the player can jump at most X tiles, and your enemies can only walk through corridors that are at least Y tiles high, etc.
Then it's time to playtest and tweak, to make the level "flow" (for instance: not bumping into walls or ceilings while jumping, and making sure escaping enemies is just difficult/easy enough). When that's done, it's time to decorate it, with the final art.
For my little "arcade" games, this workflow works well...