Firstly, who sealed it and with what...don't be affraid to ask them, by the description it sounds like a saftey flooring. Basicaly you need to strip it with remove or similar product (speak to Mike well impressed with what I have had of him) Dilute stripper as per instructions and mop on, or use a floor cloth to apply (but wear gloves) leave this to work for 10-15 mins, then srub with a scrubbing brush, and mop up with clean water until all signs of stripper and polish are gone allow to dry and mop with cleaN WATER USING A CLEAN MOP HEAD, do this a couple of times allow to dry, then once you are sure all stripper and polish residues are gone and floor is dry, apply polish, thin coates useing a window applicator, three coats should be plenty, but let each coat dry first.About half hour per coat.
Price well it depens on the size of the stairs
Petra