This is an easy procedure and you end up with a fan that looks great -- providing there is some paint there to clean and polish.
Start with dismantling the fan -- take off the blade and cage and the oscillator gear box, oilers, nuts, etc. Each part, to include the motor and base will need to be cleaned and polished -- as follows.
Using Brake Cleaner or Lacquer thinner, soak up caked grease and yuk -- may need to lightly use a tooth brush in places. The caked grease and yuk will come off. The Brake Cleaner or Lacquer thinner will not harm the brass and will only rarely harm the painted surfaces -- if there is any doubt on the paint, you should first test in an inconspicuous spot.
After the fan and its parts are free of the old grease and oil, etc., polish the painted surfaces with Meguiar’s Mirror Glaze #2 till shiny -- then follow with Meguiar’s Mirror Glaze #9. (I use the Meguiar’s products, for sure other brands of gentle compound/polish would work also.) The paint will shine -- assuming there was some paint to polish! If it does not shine, polish some more -- using more vigor. Some elbow grease may be required with both #2 and #9. After shiny, set aside and turn your efforts to the usually dead looking brass.
Take the brass items to the sink (best to use the basement sink). Determine first if any of the original clear brass lacquer is yet on the brass parts. Should you be so lucky that ALL of the original brass lacquer is yet on the brass, treat is as “paint” in the paragraph above and polish. If less than all of the clear brass lacquer is yet on the brass, use paint remover to get it off. Only very rarely will it all be in place on the brass.
Then FOR BRASS or STEEL PARTS ONLY (do not use on aluminum or painted surfaces) pour an amount of Lysol Toilet Bowl Cleaner in a glass or plastic bowl. Use the original formula in a white plastic bottle -- the new formula in the green bottle will not work. Thoroughly moisten a nice pad of 0000 steel wool with the Lysol Toilet Bowl Cleaner -- be sure to wear rubber gloves as otherwise this stuff will get you. Good moving ventilation is necessary -- otherwise this stuff will get your nose tubes too. Go after the brass -- scrubbing it fairly lightly -- or with a little more energy if required -- with the 0000 steel wool pad wet with the Lysol. Do not leave it on long -- 10 min. is OK. When looking bright, wash off in soap and hot water -- being sure to get all the Lysol off the brass. Dry with soft cloth. At this point the brass should look pretty bright generally, but might be missing some or all sheen.
Hopefully a 3450 RPM buffer is available for the next step . Buff brass parts carefully till very shiny. (Do not buff brass PLATED parts, as the buffer will quickly remove the brass plate and leave you with a steel part.) Start with brown rouge and then buff it all again with white rouge (on a new buffing pad) to remove buffing marks left by the brown rouge. It will, of course, be necessary to use heavy gloves when buffing as a great amount of heat is generated!! Then (when brass is cool), polish the brass with Brasso -- do by hand and polish to fine finish. If a buffer is not available, skip that step and go directly to the hand polish with Brasso -- this will take lots more (!) hand effort with the Brasso -- and the final result will not be as good.
Reassemble the fan. It will look great -- it may not run, but it will shine.
As should be noted, this covered clean up only -- mechanical maladies are not covered here. Often there are many of these. Among other things, it may be necessary to put on a new cord and/or headwire to finish the good look and safe operation transition. Look to Olde Tyme Radio for the great black cloth covered cord for these applications. Look to the Restoration Index for tips and instructions on mechanical restoration, etc.