You can practice book trading with the BookTrader tool of TWS in a demo or paper trading account.
An active subscription to a Level 2 data package to see market depth quotes will be required to use this tool; however, as we provide free real time quotes on Forex in most countries, you can practice with a Forex pair (ex. EUR.USD) if you are not subscribed to real time quotes.
If you are not yet an IBKR customer, use the TWS demo. If you are an IBKR customer, you can open a paper trading account, which allows you to use the full range of IBKR trading facilities in a simulated environment using real market conditions.
Visit the Paper Trading page for more details.