I came up with this idea a few years back when we were very hard up and had to decorate a Christmas table for 6 people without spending a fortune and it worked out so well, that all our place mats are now like this mainly because you can tailor them to your different colour schemes and seasonal themes and they are incredibly flat so very easy to store. They are also heat resistant, for warm plates at least.
Just raid the arts and crafts stores for your favourite kinds of papers. Thick card works well, as does some texture, however crinkle effects often get straightened out completely through the laminator. I chose a mixture of A4 iridescent green card and pearlised white paper and then created shapes out of the opposite colour and laid it on top before laminating.
You can pick up a laminator from most places for about £10-20, however one of my most prized possessions (I know, this fact is extremely goofy) is a brand new laminator that I picked up for £1 at a car boot sale - bargain! The wallets can be found fairly inexpensively at a good stationary store. Simply place your placemats-to-be into a laminating wallet and power that bad boy up. I warn you though, laminating becomes obsessive. Sooner or later, all signs surrounding you will get laminated, I guarantee it.
Once I had finished our new placemat set for the caravan, I put the scraps of paper back in the craft box and found some leftover doilies. I did warn you it can become obsessive. They came up lovely after laminating and look like plastic lace, so I popped them under our lamp and candles in the van as an easier way to clean off straying paw prints.