First, I use Davinci Resolve. In this case (i.e. Pumped Full Of Drugs), I only had to play around with the audio using DR's Fairlight page. Specifically, I used regular compression, multi-band compression, maximum stereo width, and lowered the decibel level a bit.
Most of the time DR produces massive file sizes. Once I ran the source through, it produced a file size of 5 gigabytes.
My solution to this is to then run this file through Handbrake and I usually select a preset under 'devices' that includes Dolby surround.
These are some basic elements of remastering/restoring old footage
The MOST important thing is trying to find the highest quality footage you can (searching on YouTube or surfing the web to find good footage is your best bet, but make sure it's the HIGHEST QUALITY footage you can find). There's no point in 'remastering' ultra-crappy footage; that's like dumping glitter onto a pile of dirt. There's an old adage that goes hand-in-hand with remastering footage - "Garbage in, garbage out". Basically, if the original footage of looks atrocious, there's nothing substantial you can do about it; so don't waste your time with it.
Color Correction (contrast, brightness, saturation, etc.) is very simple and can be done in most video editing software. Despite its simplicity, it is incredibly important because the colors in old footage are typically washed out and ugly. I recommend watching color correction tutorials that correlate with the editing software you're using. (e.g. I use Sony Vegas, so I can just search 'sony vegas color correction tutorial')
Post-processing (de-noising, de-blocking, grain reduction, sharpening, etc.) is yet another extremely important thing. Just like with color correction, post-processing tools are present in most video editing software.
Motion Interpolation is a technical term for artificially increasing the frame-rate of a video. In this Dreams Never End remaster, the original non-remastered footage was at 25fps, but I used Hybrid to interpolate the video to 60fps. Hybrid is a rather complicated program, but there are plenty of tutorials that will show you how to use it to interpolate videos. Just search up 'Hybrid 60fps' (or something similar) on Youtube, and you'll have no trouble finding a tutorial.