I want to be able to create my own local network using Ethereum and then I want to be able create my own currency and then trade that currency on my own local network and be able to have miners verify these trades.
I have looked at tutorials to set up a local test network and create my own currency on the Ethereum network, but it seems that there is nothing else to explain how that block would work, how the blockchain updates, and the other parts of my app.
Could someone help me?
You probably don't need or want your own local network for your own currency.
A separate network has separate everything. Separate nodes, separate smart contracts, separate ether, separate blockchain, separate miners. The main Ethereum network would be completely inaccessible. (While it would be theoretically possible for two networks to interact via a sidechain-like mechanism, I have never heard of it happening as of this writing.)
The point of Ethereum is that all sorts of applications can be on the main chain. There's no need to work out how blocks will work, because an Ethereum dapp just lives on the Ethereum chain.
What you are probably looking for/at is a currency smart contract. A currency smart contract is a simple program that records who has what balance, and allows accounts to send each other their balance. This is done by sending normal transactions on the Ethereum chain. An exchange would also be a smart contract, just a more complex one.
The point of a private testnet, as described in the tutorials, is to develop without spending ETH. Again, you probably don't need an actual separate network for the live dapp.
