No doubt you have seen the Holyhead SC website - http://www.holyheadsailingclub.org.uk . I believe it's fairly easy to get a mooring for smaller boats at the moment.
As to launching, there is a very good ramp at the club and a fair amount of car parking. For heavier and larger boats there is a boat hoist next door at Holyhead Marina http://www.holyheadmarina.co.uk where there is also a crane for mast-stepping etc.. There are also most other boatyard facilities at the marina.