Well let's start with the Signs. From your question, I'm not sure whether you are fully aware of what they are. So I'm going to give a brief technical explanation here and point you to a couple of threads on the Astrology.
The signs are a measuring system for locating the Sun and planets (including the Moon) in space, as viewed from Earth. As you know there are 12 signs and each one is divided up into 30 degrees. So in total the Zodiac forms a full circle with Earth at its centre. This circle is based on the Sun's observed path (which actually isn't a true circle) and conventionally starts from the position of the Sun at the Spring Equinox in the North. This point is defined as 0 degrees Aries. The best analogy is with a clock. We usually measure the movement of the hands from '12' and a reference such as 4:32, tells us that the hour hand is on 4 and the minute hand is just past 6. The Sun is currently at 15 degrees Scorpio. When the Sun enters Scorpio, it has already moved 210 degrees from it's position at the Spring Equinox. 15 degrees Scorpio is another 15 degrees further on, so the Sun has moved 225 degrees since the Spring Equinox. As the Sun moves at roughly 1 degree per day, it's been 225 days since Spring began in the Northern Hemisphere. During that time the Sun reached 0 degrees Cancer - 90 degrees on and the beginning of Summer, and 0 Libra 180 degrees further on than 0 Aries and the beginning of Autumn. When it reaches 0 Capricorn (270 degrees on) Winter will begin. It takes the Sun one year to complete a full circuit of the zodiac.
This same scale measuring circle can be used for all the other planets So the Moon will also pass through Scorpio. However as the Moon is much faster in it's movement than the Sun, you will see the Moon in Scorpio every 28 - 29 days. Mars on the other hand is slower, taking 2 years to do a complete circuit of the zodiac. Jupiter, Saturn and the outer planets are even slower than Mars. So at any one time you will find the planets spread out around the Zodiac circle. Mercury and Venus move at a similar speed to the Sun, so they are always within a sign (Mercury) or two signs (Venus) of the Sun.
OK the signs are simply a device to locate the planets in the sky. You will still find some Astronomers who use the zodiac as a scale but don't in any way believe in Astrology.
I'll skip the Ascendant for the moment and go on to your question on the Moon. There's two definitions of 'New Moon'. The Moon is used in some cultures and religions to fix the calendar. In these situations the 'New Moon' is the first sighting of the crescent Moon following the conjunction with the Sun (when the Moon cannot be seen).
The problem with that definition is that if it's cloudy the Moon might not be seen, so there's no precision to it. Astrologers and Astronomers use the conjunction itself - where the Moon and Sun exactly occupy the same zodiacal longitude. The last one occured when both bodies were at 3 degrees Scorpio - on the 26th October. These conjunctions can be predicted very precisely. For now it's sufficient to say they occur every 29 days
There's plenty of evidence that the Moon's cycle affects natural pheonomena on Earth such as the tides, and also animal (including human) behaviour - your biological clock may well synch with the Moon. My wife finds the Full Moon has more effect on her than the New Moon - that is it's not necessarily the same stage of the cycle with everyone but New Moons and Full Moons seem to be the main points that affect people. What it's meaning is for you is difficult to fix without knowing your chart and without you keeping a record of how you felt. It's worth your while doing that, simply to see if the pattern continues over a long period or is intermittent or even goes away after two or three cycles. Some people have intermittent effects if the New or Full Moon is very close to the positions of the Sun or Moon in their natal chart or on another key point or planet. Have you got a copy of your chart?
For more information on the Astrological meanings of signs and the Sun, Moon and Ascendant, have a look at the two threads:
http://www.tarotforum.net/showthread.php?t=166809
http://www.tarotforum.net/showthread.php?t=167024