I do a lot of concept design on paper. What is the end product (or desired function)? What sub-functions do I need to accomplish it? Break it down into as small pieces as possible and get the pieces working in their simplest form first. What are the inputs and outputs? What format or what kind of data or signals? Is there a simpler way to accomplish this? What have others done? How are the functions going to work together? How am I going to keep track of everything? Flow charts, bubble diagrams etc. can help visualize how the system is going to work together.
Don't try and make everything work the first try. Get one simple function working then save the working code or design in a separate file. Now move to the next function. Move up to the more complex functions as you learn.
You need to think about the system architecture - how all the pieces are going to work together. Look for holes in the logic and (if possible) all the combinations of inputs you might get or if the order in which you process the data matters.
How can you organize your design so that it will be easy to troubleshoot and modify? This is critical for all but the simplest designs. Document your design as you go. If you are doing the same thing in two places in code, use a functions so you don't have to correct errors in more than one place; trust me, you will forget one 
If possible, only modify a parameter in one spot in code. If more than one function can modify a parameter, think about how they might conflict with one another.
When building hardware, take the time to carefully wire and label the circuits and don't try to make the circuit super small the first time. Make a larger prototype then when the design is stable make it small.
Have a "debug function" built in from the beginning. This might be print statements if the project is SW only, a couple of spare LEDs that you can blink in different patterns in different sections of code (to see if the If/Else statements are working correctly for example) or a serial port that spits out print statements to an LCD or PC. You need to be able to see if the code is working through the logic correctly.
IMO the most important thing to remember is that you will spend a LOT more time debugging, troubleshooting and modifying the system than you will writing the original code or building the original prototype. Make that job as easy as possible and you will avoid a lot of frustration.