1 - Notebook (cheap is the best)
1 - Pen
1 - Journal (Your preference here of either something more durable than the notebook, another notebook, the same notebook, or perhaps a digital document.)
Step 1: Preparation
Before falling asleep:
Open the notebook to a blank page and set it in a place you can easily remember and reach without opening your eyes. Place the pen in an equally memorable and accessible location but separate it from the notebook to avoid accidentally dropping the pen. Keeping these items separate highly reduces my stress of losing the pen, thus freeing my mind for dream recall.
Make sure to check the ink in your pen regularly. Once, after writing down a dream, I opened my eyes to see what I wrote and saw nothing but blank pages. The ink in my pen ran out! Prevent this situation by checking the pen's ink during the day every once in a while, depending on use. Also, try to write with the pen tip facing down, unless you have a pen that can write in any position. Some pens stop inking after a few words when not in the correct position and in such a situation you'll end up with blank dreams! Preparation, aside from experience, could be done by lying in bed and testing where it's most comfortable to hold the notebook and pen and testing to see if the pen works in such positions.
Step 2: Write Upon Waking
Be as free with your writing as you can and want to be. Focus on the dream itself and not on your writing style in anticipation of legibility of your notebook. Although it is important to consider, focusing on writing style gives me a blame for cloudy dream recall. So in order to not blame writing style anticipation as a dream killer, I simply don't focus on it (to the extent possible at any given time).
Grab the notebook, which should already be turned to a blank page, and the pen and prepare your hands.
(This technique was developed for my right-handed-ness. Sorry Lefties! Perhaps you can use a clip of some sort to mark your place.)
The thumb of the left hand is used as a guide to where you are writing on the page (see images). Press the pen down onto the nail and lightly drag over to the page. This is where your line of writing should travel from left to right. Once you reach the right side of the page, move the thumb down about an inch to start a new line. Doing this keeps me from guessing my whereabouts on a page and accidentally writing over an already hard to read line of text. Most importantly, this technique allows me to comfortably keep my eyes closed while writing down what I can remember of the dream.
I find that keeping my eyes closed and writing things, immediately, is a much more successful approach to dream recollection than simply trying to remember dreams. For some people it's opposite: remember first, write later. It doesn't hurt to try both.
Step 3: From Notebook to Journal
Although this step - From Notebook to Journal - seems redundant, it is important to do and should be done right away. Why? Because the dream is still fresh in your memory and you'll find that perhaps not everything you recalled made it through in the notebook phase. Also, the sooner you transfer from the notebook to the journal the more likely it will be that you'll understand the very scribbled words in the notebook.
You can add notes and drawings in this step!
Your eyes can and should be open by now. :P
Step 4: Themes and Lucidity
If you're more interested in lucid dreaming try this instructable:
Step 5: Sleep + Write
The best advice:
Keep something with which to write down your dreams beside by your bed.
I know people who write their dreams in notebooks with their eyes open, people who type into laptops, people who type into phones. (I would advise against voice recordings. You distract yourself too much with your audible voice upon waking and the medium itself, being so dependent on time, isn't as efficient for review as a written document.) Anyway you do it, writing helps in the ability to recollect dreams. This being said from experience, not expertise.
Most Important Step: Go to sleep!