I'm not really up to speed on soldering at the moment, however my advice would be to go to Maplin and get an iron with as find a tip as possible. Worth getting something to get the old solder off the contacts - in the past I had a 'solder sucker' which is a rubber bulb with a nozzle - touch the iron to the old contacts, and slurp the solder off. You can also get braids which soak up the molten solder. You'll also need a bit of new solder - it is bought as a wire with flux already in it. Heat up the soldering iron, 'tin' the bit by melting some solder onto it before heating your component and PCB, melt on a bit of solder.