Expanding on what has been said before (but trying to still keep it simple...there's much more to all of this):
The quickest, easiest way, with what you have, is to record in Audition, one part at a time. However, from the looks of it, Audition doesn't do MIDI, so you'll want a DAW (digital audio workstation) that does. It should be able to record audio, record MIDI and host plugins (which is how you'll be using Quantum Leap) and display video. Reaper has been mentioned on the cheap (I personally don't like it). If you are Mac-based, Digital Performer is the way to go, if you are Windows based, I use Sonar, but I've heard Cubase is pretty good these days. Their MIDI implementation used to be really awful, but then again, I have some gripes with Sonar these days too. Most of them have a free trial so you can check them out, see what works best with your workflow. Many of them have "light" versions that are fairly inexpensive:
http://www.sweetwater.com/store/detail/SONARX1Ess/
http://www.sweetwater.com/store/detail/S1Artist2Bx/
http://www.sweetwater.com/store/detail/CubaseE6/
You get the point.
You will also need a good set of headphones, some good speakers and a decent interface; doubly so if you want to record some live instruments in addition to the virtual instruments (here's a tip: you do). You play guitar, so a bit of live guitar on top of a sequenced orchestra goes a long way! Then you'll need a good microphone, cables for the whole lot...did I mention this is not a cheap hobby?
Okay, so you've got the software you want to use. You've already got a controller keyboard and an orchestral library. So let's get writing!
Your DAW should be able to see your library as a VST plugin (as an "instrument" as opposed to an "effect"; more on that later). Your plugin has up to 16 channels of MIDI, which is to say, you can load up 16 different instruments and have the software play them simultaneously. Any thicker arrangements than that, and you'll have to load another instance of the plugin. We'll start basic. On channels 1-4 of the plugin, load a violin, a viola, a cello and a bass (the software provides lots of different articulations, which you'll eventually need, but we're starting basic here). In your DAW, create 4 MIDI tracks, and set the output to the plugin, and channel number 1-4. Now you've got four tracks to play, with a different instrument on each.
We'll pause for a moment...why do MIDI rather than just Audio tracks? It gives you a lot more flexibility to re-arrange and edit when you've recorded. You can go back and layer on expression and edit notes and parameters to make it sound a little more realistic. If you decide that a part might sound better on a different instrument, it's easy to switch. Furthermore, if you are collaborating, it's easy to send MIDI files back and forth. This is just the tip of the iceberg, but again, we're going basic here.
Now then, importing video. Do yourself a favor; don't work with full sized HD video. Compress the living hell out of it, reduce the resolution, make sure the framerate and audio sample rate is the same. You want to save your system resources for virtual instruments and audio tracks, and you WILL run out. Non-intuitive for a primarily visual person, but trust me on this!
Now you can see your video as you are recording. I usually set markers for hitpoints, but at the very least, where you want cues to begin and end. If you are working with a longer video, it might help to chop it up into pieces beforehand (again, you need every resource your computer has!) AudioPostExpert recently pointed out burning timecode into your video as you render, to ensure that you are dropping your score in the right places (and I still feel like an idiot for never having asked for that before). Play your parts, one at a time (or draw the notes by hand in a sheet music/piano roll view), recording the MIDI data.
Once you are happy with the music that you have, you'll need to convert the performance into audio. Depending on software, you should be able to render or bounce the MIDI data to audio. Usually you select the range and the parts that you want to bounce (so you have the option of doing the entire mix, or individual parts). Be sure to extend the range past the data, so the instruments can decay more naturally, rather than chopping off at the end.
Now you have audio; you can mix and add effects (such as reverb or EQ) and get it to sound the way you want it to. Be sure at this stage to mute the VST, otherwise you'll be hearing both the recorded audio and the instrument playing your MIDI data. When you are finished, you can export it to a .wav file, then mix in with the rest of your audio the way you usually do.
I think that covers most of the basics, but feel free to ask if you have any more specific questions, once you get going with a particular DAW. Be forewarned: there is a LOT to learn, both on the technical level and the creative level. Writing good film score is not the same as writing good music. I've been doing it for a few years now (after about 10 years experience in home recording) and I'm still a bit of a noob myself. That doesn't mean you shouldn't do it...just be prepared for a long road! Learn EVERYTHING you can from everyone you can. Ask questions. Write, write and rewrite.