What you are asking takes time to develop and core strength and stability. What is why footwork sequences can be hard, because it requires you to switch directions quickly. You will develop the skills as you get more comfortable on the ice. That being said, even when you get comfortable on the ice, falling is part of skating. It will always be there, remember you are on top of only a few millimeters of metal...
What will separate you from the crowd will be having the courage to get up and try again.
Start off slowly, but making sure that you keep a constant speed when switching directions, once you feel comfortable working at a particular speed increase it. Also, something very important skating that a lot of skaters forget, myself included, is to bend your knees. The deeper your knee bend typically the smoother the transition will be. In regards to speed, what you don't want to do is start off fast, hit your toe picks and then do a mohawk, that will end up with you face platting into the ice. What you can try to do is for example the 5 or 8 step mohawk sequences to help you get comfortable with directional changes. You'll find them on the MIF Website of the USFSA. Make sure that you work in both directions... you will always prefer one turning direction. Only working in the direction were you feel comfortable, will result in you being able to do it well in one direction, but no the other.