how do you figure out take off speed?

I assume you are refering to an airplane

Given
1-a given airplane weight at takeoff, W, pounds
2-a given wing lift coefficient, C(l), a function of the angle of attack of the wing
3-the wing planform area, S, square feet and
4-the density of air, µ, lbs./ft.^3,

From L = W = µ(S)V^2(Cl) where V = the airplane's forward velocity,

V = sqrt[2W/(µ)S(Cl))]