Let me start off with a "Hello,
My name is Nicholas, and I have a problem"
Don't know much of what I am doing, total noob, and could honestly use some advice on the subject.

I recently made the purchase of a somewhat beat up mid 80's Miyata road bike for not too much.
I had the full intentions of bringing her back to life... however, seeing as I have never done this before, I have run into a snag here and there.
I did my best to take mental snapshots (real snapshots would have worked significantly better... but whatev') of everythings placement and location, as I removed the hardware to paint the frame of the bike.
I painted it a beautiful powder blue. Simply stunning it is.
But... I've kind of screwed up.
I reinstalled the brakes/lines, drivetrain, handlebars and such components, wheels etc... no sweat.
No idea how to reinstall the derailleurs.
I think to myself in ambition... "So what! I wanted a single speed anyway!"
But of course, with no derailleurs, the chain is not in good alignment with the chainrings, and flops off after several revolutions. (Although the tension seems superb)

SO! Enough with the chit chat and on the the Q's!
Will this require a new cassette with spacers??
Or will I just need to bite the bullet, and learn how to re-install the derailleurs?
OOOooorr is there some option that my un-educated self has not yet been capable of considering?

Any help is immensely appreciated, and hopefully the more I do this, the less frustrating it will be.
By the way, I nearly died reinstalling the chain with the chain breaker. F'ing balls. I've never been so profane.

You could read-up on the options here:

https://www.sheldonbrown.com/fixed-conversion.html

Haven't done this myself but sounds like the simplist, if not the cheapest, option is to buy a track rear wheel with a flipflop hub. Your frame will most likely have near vertical dropouts so you'd also need a chain tensioner.

The Single/Fixed forum would have been the best place for this question.

Chain run alignment is the key.

I converted a regular rear to SS. The biggie in the whole recipe is to flop the big ring over onto the inside of the crank spiders. From there you need a way to line up the sprocket you want to use with that run. A ruler laid across the face of the big ring (with no chain on yet) and long enough to nearly make it back to the rear axle will soon point out where the rear sprocket needs to be located. From there it's about finding a sprocket that'll fit at that location and be the right internal size for your freewheel. In my own case I used a freehub wheel and was able to butcher some worn out cassets that the LBS was throwning out for spacers to hold the sprocket in the right place.

And since you're likely working with a 52 or 53 front ring try a 17 rear. I found that this combo worked very well for my needs. And it still just barely lets me either speed coast or grunt up 4 parkade levels when I get to work. But it's just high enough that if I have to stop for traffic I need to get off and walk to the next level.

Sounds good to me, will implement your advice and see where it takes me.
Thanks, I appreciate the help!

I do have intentions to do this later on, actually.
However I first want to do some research as to what wheels, and possibly new crankshaft I will use.
None of these I am too interested in the near future, but with my Miyata having very horizontal dropouts, it is a great candidate for a SG convert.

Please post a picture of the bike. Not every bike is WORTH converting. And people lately have been converting some really stupid **** to SS/FG just because it's the "in" thing to do.

As for singlespeed, you have two options right now which you should do given that you stated you can't put the rd on-

1) Put the RD back on
2) Run the chain on whatever chainring/cog combo that makes it straight. Shorten it (you'll need a chain tool). Then tension the wheel.

If you can't handle 1 or 2 then you really need to stop and learn how to do either of those before you even think about anything harder.