Beginning with Orchard: what to start with?
So you'd like to begin exploring Orchard because somebody sold Orchard to you. This is great! Now probably your next question is: how should I start, how can I try Orchard in action? Glad you asked. There are several simple and less simple ways, all free, so let's see. We'll start with the easy ways and build up the tension so you end up with the most complicated one if you want to become an Orchard developer.
Going on a test drive with "Try Orchard!"
No registration, no setup, nothing required, you can just go to Try Orchard!, open one of the continuously re-installed demo sites and play with it. This is the simplest way of taking the first steps with Orchard.
Be aware though that Try Orchard! is really just for testing: since the demo sites are wiped out hourly you don't try to publish your blog there!
Creating an Orchard site on DotNest
DotNest is the Orchard SaaS provider: this means that you can simply register and create Orchard websites that run in the cloud without any hassle. Your website will just work: you don't have to deploy and later upgrade it, you can just use it.
With DotNest you can try out Orchard very simply, very quickly and since your website is already hosted for you you can also show it to everybody. Apart from getting used to the user interface and features of Orchard you can also get into the basics of Orchard theme development with it and style and customize your Orchard website in a lot of ways.
Convenience does come with disadvantages: due to the architecture of DotNest you can't install custom modules, so you have to use what is already available (that however should be enough for a big part of websites).
Creating an Orchard website on Azure Web Sites
Still not very complicated but a bit more advanced than using DotNest is going with Azure Websites. On MAWS after a free registration you can create websites from the Azure Gallery where you can select Orchard to deploy in one click too.
Your Orchard site on MAWS will be completely under your control: you can install any module and theme you want too. However this also comes with responsibilities: you have to maintain your website yourself, upgrade and fix it as necessary.
Installing Orchard locally via WebMatrix
The first two options showed you the quickest ways of beginning to use Orchard that don't require you to install anything on your computer. Now we're getting into the realm of running Orchard on your local computer!
WebMatrix is a simple development toolbox that you can also use to install and run Orchard on your box, as explained in the Orchard documentation. This gives you even more control but also more work to do: you can do what you want with your local Orchard instance, you can even start writing code for your custom Orchard theme or module and run those too. From WebMatrix it's also relatively easy to deploy your Orchard site to a public host. However with this option you have to maintain your site, fix any issues that third-party modules you install may cause and you have to keep Orchard up-to-date yourself.
Running Orchard locally from the full source
This is the real hardcore option, but you'll need to do this if you want to be a black-belt Orchard developer.
You can download the full Orchard source either as a zip file from under the Releases section of the project site or you can even clone the repository via git from https://github.com/OrchardCMS/Orchard.git. You'll need Visual Studio to open, build and run the source: but since you're an aspiring developer this shouldn't be a big deal.
By using the full source you can browse through Orchard's internals to get to know it better. If you need examples you'll have all the built-in modules at hand.
Running Orchard locally and deploying it is the same as with any other web application. You can simply run Orchard by hitting (Ctrl +) F5 and it will spin up through IIS Express. If you want to get away from the simple SQL CE database option and want to use a proper database you'll have to install and configure SQL Server too. You can even use the full power of IIS and run Orchard as you would on a naked Windows Server. Getting Orchard running with IIS and SQL Server is something not trivial though.
If you're working in a team or you just want to store your code in source control things get a bit even more complicated but there are established practices that you can use.
Good luck with getting up and running with Orchard!