Pwllheli is in the top left corner of Wales on the bit that sticks out a.k.a. the Llyn Peninsular.
These online maps may help:
There are 3 ways to get to Pwllheli from the more populated parts of the UK:
North Wales Coast Route
This route has the best roads but is longer if coming from the south. Take M56 to Chester. (From Chester it takes about 2 hours, depending on the traffic.) Follow A55 along the north Wales coast. This is a good dual carriageway with only a few sections where speed is limited to 50mph (with cameras). Turn off the dual carriageway and take the A487 to Caernarfon. Follow this road through Caernarfon and after a few miles turn right on the A499 to Pwllheli. In Pwllheli turn left at the mini-roundabout and after ~200m turn right into PSC.
Mid Wales Scenic Tour
Shortest route from the south, although some roads are quite winding there are enough straight bits to make reasonable speed. Take M54 (from M6 just after Birmingham) to Shrewsbury. Follow the A5 round Oswestry and through Llangollen. (In Llangollen stop at chip shop on the left, as it takes another 2 hours from here!) After Corwen, turn left on the A494 to Bala. On entering Bala turn immediately right on A4212 to Porthmadog. Pay Rebecca 10p to cross the causeway and in the middle of Porthmadog turn left on A497 to Criccieth and Pwllheli. On entering Pwllheli turn left into PSC, before the mini-roundabout.
(As an alternative you may think about continuing along the A5 to Betws-y-coed and then taking the A470 through Ffestiniog, instead of going via Bala. Don't do it unless you really like winding roads with no passing places!)
Complete Tour of Wales
M4 to south Wales. A470 or A487 through the length of Wales eventually getting to Porthmadog. This will take a long time but the scenary can be wonderful, unless it is raining!
To investigate routes try the Railtrack web site. There are "regular" trains from Birmingham run by Central Trains and Manchester by First North Western, but you may need to change or get the bus for the last bit!
Overseas visitors are reminded that the UK rail network consists of a number of different train operating companies and for long/cross country journeys you can not necessarily buy a through ticket at the start nor rely on the connections between different companies.
From Ireland go from Dublin by Irish Ferries, or from Dun Laoghaire by Stena Line, to Holyhead which is under an hour's driving time away. Take A5 to Bangor then A487 to Caernarfon as per North Wales Route.
From Belfast there is a ferry service to Stranraer, but it is probably quicker to drive south to Dublin than all the way from one corner of Scotland into another corner of Wales.
We have negotiated a special deal with Stena for ferry travel with boat trailers.