Fractions are very simple in Mathed. Just click on the Fraction button in the Math Panel, which shows a fraction with blue squares in the numerator and the denominator. LYX writes two insertion points in a fraction. As you would expect, you can use arrow keys or the mouse to move around a fraction. Click on the top square and type ``1''. Now hit Down and type ``2''. You've made a fraction! Of course you can type anything within each of the two boxes: variables with exponents, square roots, other fractions, whatever.
Exercise: Put equation 2 of example_raw.lyx into math mode.