On a Long Distance trail like this, travelling to the start by car isn't really a good option and you might as well leave it safely at home. Not only will you find it difficult to find somewhere to leave your car for maybe up to three weeks but also this means having to travel back to Amroth or St.Dogmaels after finishing the walk, which would mean getting a bus and then 2 trains, a 3 mile walk and then you have to drive home, assuming that your battery hasn't gone flat in the meantime or been stolen.
It's easier and safer to leave your car at home rather than paying to park it some place and let the train take the strain while you think about what a great adventure you have completed. Obviously, the easiest way is to get someone to pick you up from the end and take you home but if you can't arrange that, then hopefully this advice will help.
Starting from Amroth
By Train
If you are starting the walk in Amroth and travelling by train, you will get off at Kilgetty Station and walk the 3 miles to Amroth. To get a train to Kilgetty you need to get on at Swansea or Cardiff so you will need to find trains from your local train station to get to Cardiff or Swansea, possibly changing at Manchester like I did. It's a nice way to get to the start and enjoy the scenery as you travel into Wales.
By Bus
The National Express number 508 coach from London to Haverfordwest stops at Kilgetty, which is about 3 miles walk from Amroth as does the number 528 which starts at Rochdale. There are only a couple of services daily though.
By Car
Not my preferred method of getting to the start of a walk as I don't want to be driving a long way there and back but also I don't want to worry about my car while I'm away walking and hope it hasn't been stolen or vandalised after I leave it. If you want to leave your car at the start or end, there is a National Park car park at Amroth and Poppit Sands but these are not free car parks so it could be costly.
To get to Amroth by car, take the M4 Motorway to Swansea, then the A48 to Carmarthen and then the A40 to St. Clears and finally the A477 to KIlgetty. Amroth is a 3 mile drive down the lane.
Along The Way
Once you start your walk, if you need to finish and get home for any reason, there are train stations at Saundersfoot, Tenby, Penally, Pembroke, Pembroke Dock, Milford Haven and Fishguard Harbour. If you want to miss out some days of the walk and just do certain days, there are coastal bus services, more frequent in the Summer months.
The 400 Puffin Shuttle bus travels 3 times a day in Summer, 7 days a week between St. Davids and Marloes, stopping in St. Davids, Solva, Newgale, Nolton Haven, Broad Haven, St. Brides, Marloes village and Martin's Haven and smaller places along the way.
The 404 Strumble Shuttle bus travels 3 times a day in Summer, 7 days a week between Newport and St. Davids, stopping in Newport, Dinas, Fishguard, Goodwick, Strumble Head, Abercastle, Trefin, Porthgain, Abereiddi and St. Davids and smaller places that it also passes through along the way.
The 405 Poppit Rocket bus travels 3 times a day in Summer, 7 days a week between Cardigan and Fishguard stopping in places like Cardigan, St. Dogmaels, Poppit Sands, Newport, Dinas Cross, Fishguard and smaller stops along the way.
The 387/388 Coastal Cruiser is a circular route which travels 3 times a day in Summer, 7 days a week and travels through Pembroke Dock, Pembroke, West Angle Bay, Angle, Freshwater West, Castlemartin, Bosherton, Stackpole, Freshwater East and then continues onto Pembroke Dock.
The 403 Celtic Cruiser is a circular bus route that travels every half hour in summer, 7 days a week around the St. Davids Peninsula, including stops at St. Nons, St. Justinian, Porthclais and Whitesands Beach.
The End at St. Dogmaels
When you finish, you can either walk the easy 2 miles to Cardigan town centre along a pavement or get the bus the short distance if your legs won't work after 186+ miles.
By Car
If you have left your car at St. Dogmaels or Poppit Sands car park, it'll be a long drive home. Travel to Cardigan and then take the A484 to Carmarthen, the A48 to Swansea will take you to the M4 Motorway. From here it should be easy enough for you to plan your route back home on the motorway network.
By Train
From Cardigan you can get a bus to the train station at Haverfordwest or Fishguard, and then catch a train to take you to Swansea, Cardiff or on to Manchester where you can then get a train (or bus) nearer home. Be warned though, this train takes ages to get to Manchester as it stops at about 28 stations from Haverfordwest.
By Bus
From St. Dogmaels, get the bus or walk the short distance into Cardigan then get the bus to Haverfordwest where you can get the number 508 National Express Coach to London or the 528 to Rochdale although getting the train from Haverfordwest is most likely an easier and quicker option.