How does futures trading 'work'?

Futures markets are set up to maximize clients' access to liquid markets and minimize risk.

Unlike equities markets, all futures contracts route to centralized exchanges and are matched off on a single central limit order book for that product.

For example, micro E-mini S&P (MES) futures are only traded and cleared at the CME Group. This means all MES volume ends up in one place and there is no need for a best-bid and offer requirement to ensure fair pricing.

The lifecycle of a futures order:

A trader enters an order on their screen, phone, or tablet.
The order flows directly to the exchange where it A) filled (if its a market order) or B) listed on the order book at the limit price entered. 
The order's status is relayed back to the trader and their FCM.
The FCM credits or debits the traders' account the necessary cash and positions.

Once the exchange has matched the trade, it is cleared via the CME Group's Clearing.

CME Clearing is the counterparty for every trade, which means it acts as the buyer for every seller and the seller for every buyer, thereby 'guaranteeing' the trade for both parties.