Trading on dYdX refers to opening a leveraged short or long position or cross trading via the Trade page. The trade page displays a sidebar for placing an order, any open positions, the historical price of the market and the orderbook for the market (e.g. ETH-DAI). When an order is placed, funds are automatically borrowed and traded on a third party decentralized exhange. The trade is essentially a market order - gathering the best available orders to make the trade. As part of placing an order, traders will also put up a margin deposit, which will cover them if the price moves against their trade.
Example: Opening a Long ETH Position
When opening a long position on ETH the trader will borrow DAI which is sold for ETH using liquidity displayed on the orderbook. The trader will also deposit ETH as margin which will cover any incurred losses. The trader is now leveraged long ETH. Higher leverages will result in lower margin deposits, while lower leverages will result in higher deposits.
The above example is an isolated margin trade. We address the difference between isolated vs. cross margin in a separate article titled: What is the difference between isolated and cross margin?