I was relatively new to the e-drum space back in December, so I understand your situation. I don't have a Nitro kit (mine is a DM10 MKII Pro- not a lot of people use these it turns out!), but the basics should be the same. Your question is a big one. Kinda like someone getting a car and trying to figure out how internal combustion engines work before they can drive the car. Add to that gravitational forces, temperature, moon phase and human physiology and you'll get to eventually put the car in "D" and move forward. It's not that complicated, but I understand how it can seem daunting.
So first, I am going to assume you have a laptop or other computer that's running SSD4. If you've installed it and can get sounds to work directly on the computer, then try using Reaper to use SSD as a plug-in VSTi. You can do this in Reaper by going to "Insert....Virtual Instrument on New Track..." then select your SSD plug-in. I use Addictive Drums 2, but the process should be the same. Reaper will ask how you want to route the plug-in tracks. Make your selection (in AD2, I route all outputs from my VST as separate tracks. You can also select a stereo-only routing, which might be preferable as you learn how these things work for you).
Now, as for Reaper seeing your Alesis module as a MIDI device, you need to go to "Preferences" and select AUDIO>>MIDI DEVICES and find your module. It should be listed there if your system setup is configured properly. I am a Mac user, so I just plugged it in and the Core Audio did the rest. I can't help you set this part up in a Windows environment, though I'm sure there are plenty of people on here who can chime in if that's the case.
Okay, let's pretend you've been successful in adding the SSD plug-in to a reaper track. You should be able to play various instruments (drum kit pieces) in the VSTi plug-in window. Again, I'm not sure how SSD integrates, but if it's VST/AU or RTAS-capable, then the setup should be the same for any plug-in. If you get banging sounds (e.g. drums) coming through your headphones, step one is done!
Now you need to figure out if you have enough RAM on your computer to play things without latency. This can be a problem, as this kind of setup does tend to eat your CPU's memory. I tried doing it with a Macbook AIR that only had 2 Gigs of RAM (my new one has 8 gig and works flawlessly), and despite my playing with buffer size settings, I was getting either distortion, or clicks and pops as my system tried to keep up. I ended up getting an EXTERNAL USB AUDIO INTERFACE to alleviate this issue. It works as a "external sound card," to allow better throughput of audio information. They are obviously USB-capable, and depending on the model you get, will have inputs and outputs for a variety of sources. I selected a Behringer UMC404HD. I love this thing! It was relatively inexpensive for what it accomplishes ($129 with a Musician's Friend coupon). I plug my iTunes source (for play-along tracks) into the Main inputs on the front of the unit, then run the USB to my computer. My Alesis module runs USB out to the computer (I don't use the midi ports). The Audio/Midi setup on my Mac does the rest insofar as routing the signals to and from the appropriate devices. Like I said, you can tinker with these settings in that utility if things aren't making noise. It just takes a little bit of poking around to get things up and running. Again, if you are running Windows, the basics are probably similar, but the specifics aren't something I can comment on.
Once you get your module and VST (SSD4) recognized by Reaper, you can start playing around with the functions of Reaper. They have a pretty useful forum on their site for user-specific issues. It's a really good program. I tried out Pro Tools, and that thing is a nightmare compared to Reaper. At least in my experience. It's powerful, inexpensive and it feels intuitive once you get used to the big picture of digital audio and computer/external source integration. Using a Digital Audio Workstation (DAW) is a whole other topic unrelated to getting your hardware working properly, but just play around once you get appropriate signals. There are a ton of settings and options in Reaper that can feel ovewhelming, but if you just focus on recording tracks, it's similar to any other recording device. You can start playing with other effects, track adjustments, output options, etc., as you get comfortable with its workflow. I entered this realm not too long ago, but I'm finding it pretty easy to navigate and troubleshoot once things are up and running. I'm sure there folks on here who can speak with more eloquence and technical expertise about your issues, but I thought I'd chime in with another Newbie perspective.
Good luck!