→ ToC and first chapter.
How, when, with what, and in which stages
Stages
At first, draw a graph of a level. it can be just a named sequence of nodes — locations —, or it can be a more complex structure, depending on the game and your ideas.
If necessary, the graph is detailed and turned into a more detailed diagram/drawing.
After that, these nodes are placed in the game engine with simple figures (aka blocking out or greyboxing), with the addition of basic landscape details, cover points, placeholders for notable landmarks, and plot stages, but with all the gameplay elements.
After the initial layout, playtests take place, after which the level is either thrown into the trash bin or finalized to a playable state.
The level is implemented as it should look in the final game. But even after that, you need to test the level at least once more — new details can disrupt navigation, hide or reveal important details, add alternative paths, etc.
So:
Draw a graph → Add details → Blockout → Playtest gameplay → Finish visuals → Playtest again
With what
It is best to design a level on paper. A simple graphic editor with an emphasis on the drawing process can serve as a digital substitute. For example, Autodesk Sketchbook or Krita. For 3D levels with strict shapes, Magica Voxel can help.