Like Chuff says, M54 to Shrewsbury, then straight up the A5, past Betws-y-Coed. There are sections when you'll just have to follow the lorries, but it'll be like that which ever way you go through Welsh Wales. Just enjoy the views, you'll get there in the end.
If you want to drive faster, you could head on up to Wrexham and onto Chester, follow the A55 across the top of Wales, the drop down into Llanberis, but that is miles out of your way and would probably take longer.