For those who are new to growing Shiitakes I just want to give some followup information on what to do with your log once you get it home. Most of this information is my personal opinion based on a fair amount of reading and a little bit of actual growing experience - take it for what it's worth.
The most important thing is to not let the log dry out! The moisture content needs to be above 30% or the mycelium (the part of the fungus that is growing inside the log) will not be able to thrive. I'll try to put the moisture content in some kind of context. There is a rule of thumb that is used by wood workers when air-drying lumber that it takes (depending on species) approximately one year per inch of thickness to dry a board to about 15% moisture content in an unheated space. This does not tell the whole story though because wood gives up most of its moisture in the first few months of the drying process. Much of the moisture in a tree is not bound inside of the trees cells, this "free" water is given up much faster to evaporation. Once the wood gets to about 30% moisture content, the free water has evaporated and the remaining moisture has to migrate out of the cell walls to evaporate. The time it takes a board to go from 60% moisture content down to 30% is less than the time to go from 30% to 15%. In order to stay above 30% moisture content we are keeping our logs above what is known as, the fiber saturation point (the log still has free water.) The good news is that there are several important differences between trying to dry boards and trying not to dry a log. The first is that boards don't have bark and the second is that someone who is trying to dry a stack of lumber is not going to let it get wet.
The bark of your log is very important in slowing the evaporative proccess. You will notice cracks on the ends of the logs where the wood has already dropped below the fiber saturation point and begun to shrink due to water migrating out of the cell walls. Logs lose moisture much, much, faster out the ends than they do from the sides - especially when they retain their bark. Don't worry about small cracks on the ends of the logs - that is why we cut them so long (to help retain moisture in the center of the log.) The logs will also soak in water much faster from the ends so you want to make sure that they have access to rain while you are letting the mycelium grow.
What it all means in the context of growing Shiitakes
As long as you put your log in a place that receives 75 - 100% shade, protect it from wind (which speeds evaporation) and allow it to receive rainfall you will probably not need to do anything to the log until summertime - when the heat speeds evaporation and rains can be few and far between - when you will need to water. If we get an unusually dry spring and fall you will also want to water your log(s.) To water you can run a sprinkler on them for several hours or you can soak them for an hour or two. If you have chlorinated water you will want to use the soaking method (fill your container the day before and allow the chlorine to off-gas before soaking your log.) I use a trash can to soak my logs - they stick out the top so I just flip them over halfway through. These periodic short soakings are just to maintain an appropriate moisture content that promotes good mycelium growth.
Fruiting your logs
You may see a mushroom or two (make sure you know how to identify a Shiitake) the first fall after inoculating your log. If so you can consider that the icing on your cake or, perhaps the butter on your morels. It is just as likely that no mushrooms will appear on your log until the following spring after daytime temperatures are in the seventies for a few weeks. Once you see a mushroom or two start to poke out of the log you know that it is time to shock the log by soaking it for 24 hours in the coldest water available. Once again if you have chlorinated water be sure to let it off-gas before soaking the log. After you have soaked the log place it upright or lean it against something so that you can reach all of the mushrooms that will soon be popping out.
Good luck!
More info. on growing Shiitakes. blogs.cornell.edu/mushrooms/files/2014/03/Shiitake-BMP-3-11-1osfnxs.pdf
More info. on air drying lumber. www.fpl.fs.fed.us/documnts/fplgtr/fplgtr117.pdf