Many right-handed flycasters have a natural curve to the left because of delivering the fly in this manner. Place some Frisbees or plates on the lawn as targets at different ranges. Try to make your left curve cast snap behind these pretend rocks and protuberances. Presenting the negative or right curve cast is a bit more challenging and takes more practice to become accurate. This is an underpowered cast that is made with a slight hand movement from right to left on the horizontal plane.
Practice begins again with regular false casting to the front.
On your presentation, ease off on your stroke, bring your line in low, and sweep your rod from right to left as your loop is forming off the rod tip. As you aim at your targets, try to drop your yarn fly right over them. An advantage of this right curve is that it lands softly, but it is nearly impossible to use in a wind. You can spend hours working on presentation casts, and the reach cast popularized by Doug Swisher should be a standard. Once you learn this cast, you will never fear regular currents.