I will suggest starting right here on Mahalo where there is a very informative page referencing morel mushrooms.
http://www.mahalo.com/morel-mushrooms

I've been an avid morel mushroom collector since I was old enough to walk in the woods so I do have conciderable knowledge on these delectible springtime delights of nature.
As for what time of the year is best to look for morels depends alot on what part of the country you are searching for them. Morels come up according to many factors and with abit of research of the links I'm providing you can gain good knowledge of when and where to look for them.

If you have never hunted morels before I would suggest joining one of the morel hunter forums such as http://morelhunters.com/
and getting aquainted with a few seasoned mushroom hunters in your area.
They are for the most part quite willing to help people with learning how to find morels.
With a little help and pratice you will soon be finding morels to enjoy.
A word of caution, hunting morels can be addictive!
Its an addiction well worth the time though.
Over time you may find yourself graduate into hunting the many other types of edible fungus that extends your mushrooming throughout the year and adds enrichment to your dining experience.

We enjoyed a rather good morel season here in mid Missouri this year which typically begins in late march and runs into early may.
Here are a couple of pictures of a few of my 2010 finds,





http://www.youtube.com/watch?v=aNh_RC5rSm4&feature=related

Good luck and if your ever in my neck of the woods during morel season feel free to get in touch, we often take new mushroom hunters out on hunts and show them what we know.

I found this site dedicated to the hunting, preservation, cooking, and so forth of morel mushrooms:
http://morelsandmore.com/howtohuntformorelmushrooms.htm

Now to answer your question:
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Morel Mushrooms will grow when the temperature, humidity, variance between daytime and nighttime temperature, soil acidity and many other factors are JUST RIGHT. The "season" for Morel Mushrooms begins sooner in the southern climes and works its way north as the daytime temperatures get warmer sooner. If you live in the southern hemisphere this trend is reversed.

When temperatures in your area in the Spring begin to climb into the sixties during the day and are no colder than the forties at night (Normally April in the Central United States) Right after a rain is when I have found it to be the best. You should look in stream and river beds, wooded areas, around fallen timber that has been decaying, and don't forget to look within brambles and thick underbrush.
----/quote----

Hope this helps!

Well, I live in the morel mushroom capital of the US. Here you can usually find mushrooms during the month of May, maybe even late April or early June, depending on the rain and wear you search for them. During the month of May we have our annual Mushroom festival, that is usually around the time everyone goes out hunting for morels. You can find them usually after a good rain. They tend to hide near brush and fallen timber or near streams. I often find them on the side of small hills or in shadier places. You may need a good eye though, some can seem to camoflauge amongst leaves and things so don't step too fast.