First, I start to read the requirements and documentations and try to get a rough sketch. This is mostly done inside my head and partly on paper. (I have a very good memory.) The first phase of the design is often done away from my computer! Ideas might pop up in my head while I'm in the car. Sometimes, I'm even getting new ideas while dumping something smelly in a large, porcelain pot in a very small, locked room. In general, the design ideas tend to pup up when it's quiet and I have a chance to let my mind wander around a bit.
Almost two years ago, I did have a big project that needed to be designed. Another developer had been working on this already but became utterly frustrated by it, to just leave the company simply because after several weeks he still hadn't found a good solution. So, then it was my turn...
I had the advantage that I could work at home, so I did. I've spent the first day of designing in my bedroom, in bed with pen, paper and documents. I had the notes from my former colleague and could see that he made things far too complex so I started to divide the problem in smaller steps. I continued wasting paper making notes, doing calculations in my head and comparing my notes with the documentation and other notes. That first day, I never used my computer.
The second day, I started to type a technical design and write some code to test a few principles. I still spent a lot of time away from my computer, though, taking short naps in-between to take some breaks from the heavy thinking. It took the whole day but in the end, I had the whole concept finished on paper.
The third day, I had my concept printed and shared it with my teammates. While I continued to set up the basic requirements for the code, they could start judging my design and point out the flaws. That day, they didn't find any, although I did leave a few in it.
The next day, a teammate and me started to implement the Proof-Of-Concept code that would be needed to get it all to work. Within two more weeks, the whole beta-version was finished and just needed some tune-ups. This was something the rest of the team would do, while I went on a holiday.
After returning from my holiday, the whole project turned out to be a great success and the functionality was very well-received by our customers!
So, required materials: small rooms, pen, paper, a bed, lots of coffee, food and relaxation. Stay away from the computer and be lazy. (By lazy, I mean: avoid writing code immediately. Just think, which will make people think you're just doing nothing...)
When designing something for others to implement, you will need out the first part of the design yourself, as complete as possible. Just stick to the big things, allowing room for little things to be added by your team. And most important: rely on your team to take over your job at a certain point and be prepared to step back once they start moving!