If it is a used, wooden grape press like the one pictured here's the "gold standard" of how to get it back to good condition and keep it that way:
Remove the wooden parts from the frame and soak them in warm sodium percarbonate for a day or so.
Remove the parts from the solution and hot pressure wash them as per Grott's suggestion.
Dry them out thoroughly, preferably in a kiln and replace any that crack or split. Preferred wood is oak but you can use anything really, see the next step.
Buy a kilo or so of coating wax*, melt in an appropriate container (an old electric frypan works really well) and paint all the surfaces of the wood with two coats.
Meanwhile, repaint the steel parts of the frame (except the main screw) with a food grade epoxy paint.
Clean the main screw and the bronze nut in which it runs and regrease them with food grade grease. Since you may have trouble buying small quantities of this, PM me and I'll send you 50 g or so. Another treatment that works really well is to coat the screw (but not the nut) with a layer of grape seed oil and allow it to harden (warmth and oxygen).
Reassemble using stainless steel fasteners.
Clean your press immediately after every use; do not allow it to dry. Do an extra clean at the end of vintage, then immediately before the next vintage clean it again and apply a new layer of wax.
This sounds like a lot of palaver but badly maintained presses are a real problem. By now you may understand why the industry uses stainless steel presses almost exclusively.
* winery supplies sell coating wax for this purpose (and for coating concrete fermenters). Don't use sealing wax. Plain beeswax is OK.
