After creating an account and funding it, select a market to trade from the drop down and a quote duration by clicking on the appropriate duration you are looking for:
In this case the trader has chosen ETH/USD as the currency exchange rate to trade, and 1 hour for the quote duration.
To place a quote, hover the mouse on the left hand side of the chart so you get a set of three horizontal dotted lines similar to the following screenshot. The spot price (A) is the purple line and can be changed by moving the mouse up or down. The premium (B - one above, one below) is indicated by the dotted horizontal lines located at equal distance above and below the spot. These lines indicate the ask premium for the quote.
Note that the ask premium is not necessarily the premium that will be paid by the buyer. The solid green bar (D) and solid red bar (E) indicate the approximate discounted or increased premium the quote will look like if placed on the market. These premiums are modified proportionally to how far the quote's spot lies from the current consensus, and will change automatically with each market tick (see Microtick Quotes as Options for more information)
Finally, notice in some cases that the intersection between the green and red bars is slightly above or below the current consensus. This is a visual indicator of how much placing the quote will affect the consensus price. If your quote does not modify the consensus price at all, try either increasing the backing by clicking and modifying the backing in the dialog, or decreasing the premium range (the distance between lines A and B).
When you click on the mouse, a dialog will pop up allowing you to fine tune the Backing, Spot and Premium values manually before placing the quote (or canceling, in which case the backing setting will stay what you set it to on the dialog the next time you hover over the chart).
Once the quote is placed, a table row will appear with the quote's settings, along with a set of controls to modify the quote (change the Spot, Premium, Cancel the quote, or Deposit more backing). When you change quote settings, a time delay of at least 30 seconds is enforced before the quote can be changed again.