I played around with Monogame for a long time, but had a lot of trouble getting shaders working as well as figuring out all the nuances of content. It’s finally matured enough as a development system that it’s relatively straight forward to get it working now. That said though there are a few steps. First off, this as of June 2015. The process might change if you’re reading this years later. I recommend going to the websites and following the direct instructions there as they may have changed since writing this. Again, I do my best to point anything out, but follow this at your own risk ;). That said though, this got me up and running in monogame in under an hour.
My Set up
I’m developing games for both windows and linux. I have a windows laptop and a linux box (actually technically a chromebook running crouton, but it get’s the job done). I have most of my code syncing between my dropbox folders, so any changes done in the windows version will be automatically synced with the linux version. I also use the same solution file between both environments. This is what works for me, I’m a single developer, so I don’t need ot worry about Git or anything. It’s simple, and it works. But I’m sure some people have their own way of doing things.
Installing Monodevlop/Xaramin Studio (Windows)
On windows, I simply just installed Xaramin Studio from the monodevlop site.
Installing Monodevlop/Xaramin Studio (Ubuntu)
For linux, namely ubuntu, it’s a little more involved and involves some command line fun. Got to the download section on monodevlops site and scroll down to the Linux section. For this tutorial I am installing on Ubuntu. 
Before you can install monodevlop, you need to install mono if it hasn’t been installed yet. Clicking on the link for Debian, Ubuntu and derivatives take you to a page with instructions based off of your version and distro, follow those and then come back to this page below. 
Once all of the mono libraries are installed, it’s time to install monodevlop. In the terminal type sudo apt-get install monodevelop to install monodevlop. Install any other items you might want shown on the page above. Once monodevlop is installed, start it up.
The Main Event (Both Windows and Ubuntu)
Now to get to the meat and potatoes, the main event, the turkey dinner after the warmed up appetizers. To get monogame installed. Navigate to: Tools >> Add-In Manager 
Then Navigate too: Gallery >> Game Devlopment >> MonoGame Addin And click install. The installation process takes very little time. 
You can confirm it installed by looking under: Installed >> Game Devlopment 
And that’s it. Start a new monogame solution and test that it works. My windows installation started right away, but my linux install gave an error the first time and required a few more libraries installed. This didn’t happen the first time I installed it under linux, but it did the second time. Unfortunately this is a case by case basis, so if you find you’re missing something, google online and find how to install it. 
Once you have everything up and running, you can start a new monogame project. Run the project and should see the ever so famous Cornflour Blue default background.
So that’s it. If you have any questions, let me know in the comments. I’ll be posting more tutorials in the coming weeks.