"Standard form" really depends on what you are referring to. The standard form for conics is very different from that for quadratic equations. For polynomial equations, you would generally write one side of the equation as 0 and the other side as the terms listed in descending order of degree, such as 4x4 -3x3 -9x2 + 6x + 7 = 0.
Assuming that you refer to linear equations, Standard Form is Ax + By = C, where A and B are integer coefficients, C is an integer constant, and the x and y variables are on the same side of the equation. An example would be: 3x + 4y = 7
To convert slope-intercept form to standard form, you would first multiply both sides of the equation by the least common denominator if there are any fractions. For example, if you start with y = -3/4x + 7/4 you would then multiply both sides by 4:
4y = -3x + 7
Then you would move the x variable so the y and x variables are on the same side of the equation and the constant is isolated:
4y + 3x = 7
3x + 4y = 7
*As a note, more specific questions usually receive clearer answers:)