To do it right, you will need to strip this bike down to the bare frame, replace all bearings, tires, brake pads, cables, housings, etc, true the wheels, new bar tape and lever hoods.
This requires some bicycle specific tools, or an occasional trip to your favorite bike shop for some disassembly (which is not a bad option). Much like working on a motorbike, you can damage vintage parts if you use the wrong tool for the job.
Removing pedals is best done with a pedal wrench, or just have the shop do it for you.
Use the search function on this forum, be sure to check the box sort by relevance. And search youtube and the parktool web site. Lots of info out there.