Draw whatever shapes you intend to paint with a hard lead pencil, 4H or harder. Hard lead pencils will make light marks that are easy to cover up later with pigment, and easy to erase if you make a mistake. Use a ruler when drawing straight edges, and if necessary, use a compass when drawing circles.
Limit the amount of water you mix with pigment on your palette. By limiting the amount of water you mix with pigment, you make the paint less runny and more easily controlled. There is a draw back to this -- water will often dilute the color of the pigment and give the paint a softer, lighter quality. By limiting the amount of water you mix with the pigment, you're more likely to have darker, bolder colors. If you were hoping for lighter, softer colors, you may need to mix in white watercolor paint.
Mask the edges of each shape you're painting with masking tape. This will only work for shapes that have a straight edge. To prevent the masking tape from fusing to the paper, try sticking and unsticking it to your clothes a few times before applying it to the watercolor paper. For detailed edges, you can also apply masking fluid -- found at art stores -- to the paper.
Choose smaller brushes to paint with, to allow you to control the edge of the paint much better than larger brushes. If you're painting a large shape, paint the edges of the shape with a small brush, then switch to a larger brush for the center of the shape. Remember that watercolors applied at different times can dry at different speeds, so if you wish to keep the shape looking uniform, paint the inside of the shape quickly before the edges have had a chance to dry. Blend the two applications of paint with a dry brush.
Wait for the paint to dry before moving on to different shapes on the same paper. This will prevent the water from flowing from one shape into another shape as you paint. Paint on dry paper only -- do not paint on a wet surface. Paint applied to a wet surface will bleed uncontrollably all over the paper, and you will have very little control over the shape the paint takes.