Adjust your high and low limit screws as described or see parktool.com for front and rear derailleur adjustment. If the limits are set correctly, you're 90% there.
Next step - Adjust cable tension. The fder spring is constantly applying pressure to bring the fder back towards the seattube. Cable tension controls this. Inadequate tension results in the chain snapping back towards the seattube, sometimes resulting in chain derailment. Increasing chain tension will remedy this. If you have an adjuster on your fder cable, turn it counterclockwise to increase tension. This adjustment is crucial to fine-tune your shifting, allowing up and downshifts to seat properly on the chainrings.
Don't forget to check the height of the fder and the angle of the fder relative to the outer chainring as well. 1-3 mm vertical clearance and parallel or very slightly toed-in for best shifting.