Write the formula appropriate to the type of support the beam has. For a cantilever beam with one support, such as a beam attached to a wall with a load applied to the free end, this is D = FL^3 / 3EI. For a centrally loaded beam with a simple support on either end, it is D = FL^3 / 48EI. In the same situation where the load is not applied to the center, it is D = Fa^2(L - a)^2 / 3EIL. These are by far the most common situations, but for other situations, you can easily look up the appropriate formula. D is the deflection, or how far the beam has been bent, F is the force applied, L is the length of the beam, E is the Young's modulus of the beam, I is the moment of inertia, and a is the distance from the closest support to the applied force.
Using basic algebra, rearrange the equation so that F is by itself on the left-hand side of the equation. Formulas for bending a beam are usually given with the deflection, D, on the left-hand side, so if what you actually want to know is the force, F, as in this case, you have to rearrange the equation. For example, D = FL^3/3EI rearranges to F = 3DEI / L^3.
Find the moment of inertia. Use the cross-sectional type of the beam to find the appropriate formula. For example, for a rectangular cross-section, the moment of inertia is found with the formula I = wh^3/12, where I is the moment of inertia, w is the width of the beam, and h is the height of the beam.
Plug values into the equation and perform the calculations until you have a result for F.