The guys & gals making thin wallets will skive all the edges of the card pockets & the edges of the main body of the wallet to achieve a thin wallet.
Certain card pockets shapes also help with keeping the wallet thin.
I started out with a leather kit from Amazon. It was like $140 & had all the basic tools to get started.
Plus it had 4 colors of thread, beeswax plus some other stuff.
I made a lot of stuff with that kit.