Its a tricky thing Rhiannon because beaches can be littered with all sorts of stones from all over the world.
If you are focusing on one particular beach or gegraphical area then as a starting point I would try to familiarise yourself with the bedrock geology, particularly those layers that may be contributing material to the beach through erosion e.g. If you are anywhere near Chalk then you are likely to have beaches covered in flint and chert pebbles. Another factor is long shore drift, which basically relates to the dominant wave direction pushing material along the coast generally in one direction. Taking in long shore drift can help identify some pebbles that mgiht come from a slightly extended geographical area. Round my way there are beautiful purple quartzite pebbles that all come from one layer of rock that is being eroded on the coast about 50 miles to the west.
If you can get your head around the local stuff you'll have a basline knowldge that will help you spot the more unusual material... and as I said that can include all kinds of stone.
Typically only really hard stuff lasts long enought to travel very far, or last a long time on a beach, meaning you're probablylooking at igneous and metamorphic rocks for the exotic pebbles you might come across. Watch out for man made material that has been rounded off - brick, concrete, tarmac etc. I'd also reccomend checking out any rock armour near to where you have collected things. That stuff might have come from miles away. A popular one is a dark, hard rock from Norway that appears a little like granite and has nice big crystals in it that can shimmer blue/green... I forget its proper name... anyway bits can get knowcked off that sort of things and end up in the pebbles. The other main source of oddities is ships ballast that has been dumped or washed out of wrecks. This can obviously tie into some pretty cool scocial history and come from anywhere in the world.
none of this is very helpful as a simply guide to identifying pebbloes... but I hope you can see that what you can find is so messy that its best to start with a process of elimination rahter than outright identification.