The Grill Grate
One object that determines the shape and size of your outdoor river rock grill is the metal grill itself. If you are using a round grill frame, then you are going to be constructing a round rock grill that is similar to a fire pit. For rectangular or square grills, the shape of the rock formation will need to have straight sides to match. Whether circular or rectangular, the front side of the grill is left open for access underneath. A rectangular grill would have three sides under the grill area, and a round one would leave a gap, not fully closing the circle. To determine the inside edge of the grill area, lay the grate down in the location you want to build and mark the outer edge with spray paint.
Planning
Plan your overall design for the grill. Whether it's round or rectangular, will want the entire grill enclosed below the grate and a pit of gravel below to catch drippings and hold the coals. Consider building up the back of the grill to catch splatters from sizzling meats and adding a little height to the sides to cut down on wind disturbances. You could also build the sides wider than one rock thick and create a platform for a plate or grill utensils to rest.
Foundation
The foundation of your grill starts with a trench to hold gravel, as well as the first course of river rock. The gravel keeps water away from the base of the grill. The width of the trench should equal the overall width of the rocks. The depth should match the average height of the rocks plus 8 inches for gravel and cement. If you are creating a wider grill to form a platform for a plate, create a trench wide enough to hold three or four rows. Once dug, fill the space with 2 inches of gravel and pack it down. Over top the gravel, pour 6 inches of cement and allow it to cure for two days. After the concrete has hardened, place the first layer of river rock in the trench, using mortar to anchor it to the concrete.
Construction
To form your grill, add more rows of rock on top of the first. Since river rocks are not one particular shape or size, you will need to choose rocks that are similar to form the row. Mix a batch of mortar and apply it between rows and ends where rocks meet to hold them in place. Once you get the grill at the height you would like, add some metal brackets to the mortar, so that they stick out into the open area in the middle. These will help hold your first grate. Add another row or two of rock above, depending on the size of the rock, and then repeat the clips for the grill grate. With the second set of metal brackets done, place at least one additional row of river rocks on top to complete the grill. Fill the inside of the open area with 4 inches of crushed gravel. The small rocks will absorb drippings and are easily dug out and replaced when necessary. As another option, you could add an additional set of clips below the coal grate and install a tray to catch the ashes.