How to complete a Scheffe's test by hand?

I have ANOVA output for statistics, and the necessary formulas (I think?) but I can’t figure out all of the variables (what gets plugged in where), and what I need to compare to do a Scheffe’s test. I’ve gone through my class notes, my lab notes, my textbook, and have been googling like a fiend, but I’m still utterly confused.

I know to find my F value, I need to divide the SS contrast by means squared within groups, and I have the denominator from ANOVA, but I’m not sure how to find the SS contrast.

I know SS contrast is L(squared) over the sum of ci(squared) divided by ni, but I’m not sure what values to plug in to find the SS contrast. There’s also ci (i is subscript) in the formula for L, and I have no idea what it represents.

I think I’m good on Scheffe’s f (the f critical) because you take the number of groups and subtract 1, then multiply by the critical value you get from degrees of freedom and alpha. I got (4–1)2.60=7.8, so I’m all right there.

Basically, I have no idea how to come up with the calculated value so I can compare to the critical value for significance. PLEASE help!