So you get that 'new' old reel home & take the spool off, only to find it loaded with dirt, old grease, & a bunch of gunk. It needs a good cleaning. There are several ways to do this, & the video below shows a very safe method of getting the old dirt off of a vintage reel. If you're not advanced in your skills of working with fly reels, than I'd suggest you follow all the procedure outlined in this video.
The second part of the video shows you how to lubricate the reel, once its cleaned & dry. Again, if you follow the examples in the video, you'll be fine. I, however, would make a few different maneuvers with my own reel. For example, in the video he only uses oil to lubricate everything. That's fine, but oil can (& will) eventually leak out into the other parts of the reel. I prefer to use grease on the main post, or spindle shaft, of the reel so that the spool is always spinning on grease. I also prefer to grease the teeth of the drag arbor gear at the bottom of the post. This is just a personal preference & you will find pros & cons about the use of oil vs grease for all applications (engineers have been debating this for a very long time).
One other tip from me: in addition to using cotton swabs to clean the reel, an old toothbrush is also a great thing to use for this kind of work. It can get into places a rag or swab can't, such as in between the teeth on gears, etc.
So if you're trying to pass the cold winter evenings by cleaning up some old reels but aren't sure where to begin or if you're doing it well, check out this video below. It's a very good, safe, guide on how to maintain those old reels to keep them spinning for many seasons to come!