Hi, Irised! I moved this over to our Working With The Moon forum, I thought it was an excellent question to ask. I would love to hear how others use this time as well.
The new moon is my favorite time for breaking out the tarot cards. And the sage. And the feather duster.

I am sure many of us like this time for cleaning, even if it involves a mop (and broom, hehe) or a good, deep spiritual cleansing, this is a great time for it.
I like to change or add to my altar at this time, after a good cleaning both mundane and spiritual. Maybe make some changes for the coming month or season or just whatever feels right at the time. It sets the tone for me for the upcoming month.
Since I do not cast circles I feel it is important to cleanse my space regularly (my bedroom, altar, tools, everything...) every new moon. It is one practice I always have to do, or I just don't feel right. I also take a cleansing shower/bath ritual of some sort, even if it is quick and simple.
If I have an important spell in mind that I feel may be needed, I like to start the process on the new moon. Planning to work the spell on the full moon, I use this time for divination for the issue, to plan and write and gather items needed. Really I only go through this process maybe a few times a year, for serious needs or issues or a certain moon that I really want to draw from.
I also have a small lantern on my altar with a battery operated votive candle, which I will leave on during the darkest nights of this moon phase while I sleep.
I really love the new moon phase. A great time for a fresh start, new beginnings and hope. Cleaning out the old and regaining focus. Setting intentions and letting go of what does not serve you.
Create, Release, Renew, Begin.
