If the watch is simply losing or gaining time, then it needs to be adjusted. Any competent watchmaker/jeweller should be able to do this - most mechanical watches have an easy setting mechanism to change its amplitude.
However, if the watch is stopping, or not behaving correctly, then you'll need to get it serviced. The cost of this will depend on whether you get an authorised reseller to do the job or if you go to a watchmakers. In general automatic movements need servicing every 5 years - the different types of oil used in the watch shift over time.
For a basic service, the authorised job could cost from 200 to 1000. the watch maker will probably charge from 100-200 for a basic service (disassemble, clean, re-oil, reassemble). There may be more bells and whistles on an authorised service e.g. polishing/refinishing of watch case, verification of seals etc. But as with anything, check what you're getting for your money.
I've used the guy on exchequer st. (up from Weirs) with good results - check the yellow pages under watchmakers for other options and ring around for a price.
Al