I'll jump in. I've long used a program called "Keynote NF" for basic note taking. It has tabs and hierarchy and means that I have a good place to put anything I think of as soon as I think of it.
To start a design you take notes. Write the requirements, identify questions and start brainstorming the design. Search out any examples of similar designs you can find and take notes on them - what topologies, components or techniques did they use.
Then when you have ideas of how to approach the problem draw pictures (I use visio for diagrams). Try to draw multiple complete pictures and, importantly, compare the pictures as a whole. Often an early choice might seem wrong but open other possibilities later.
When doing detailed design again I rely on notes. Each major circuit gets a section so I have a place to put any questions or ideas that come up as I'm designing it (I.E. check ripple rating on input cap).
Peer review is important. In general I like reviews to happen here:
-Concept review answers "what do I plan to do". Includes major components, topology choice, number of PCBs etc.
-Design review answers "how am I doing it". Includes complete schematics and preliminary layout and/or placement.
-A final design review vets out details, component vales and layout.
Checking designs is its own art. One thing new people sometimes don't appreciate is that everything can and will go wrong. The schematics for 2 mating connectors may be correct but there are still about 12 things that can go wrong and prevent them from mating (incorrect part numbers, footprint error, connector orientation etc). To check connectors for example I check the two layouts to verify that the signal names of the mating pins actually match. Better: Print 1:1 sized printouts of the layouts, glue sample connectors onto them and check that they mate.