just sand the sucker down by hand..no tools as this will make marks that show..only sand with the grain ..not across or there will be trouble.wipe down the stain and oil...couple of hours will do it...sholud get those water stains out anyway..let us have an after pic please.choose a light stain .it makes ya kitchen look cleaner.
I agree with everyone here.A good sanding using a powered sander using an 80 grit paper with lots of paper changes,followed by powered to 120grit and hand sand [as MrG says WITH the grain ]to 180 or 240 grit.
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Agree with the sanding to get the top stuff off - then apply oil with either fine wire wool or scotchbrite, I did this with our old worktop (which was cherry btw) and it came up beautifully....
Whatever you/they do it will involve plenty of elbow grease, definitely worth it though.