Beyond the more geometric methods explained so far, there is an iterative algorithm (in practice, as precise as any exact method) due to Shuzo Fujimoto that I think no one mentioned. In fact, the following method can be generalized to any shape, size and number of foldings.
Let me denote $d_l$ the distance from the left side of the paper to the first mark on the left and $d_r$, the distance from the right side to the right mark. To simplify, assume that the lenght of the side you want to divide is 1.
Make a first approximation for $d_l$. You want $1/3$, but imagine you take $1/3+\varepsilon$ ($\varepsilon$ being some error to the right or to the left). Thus, on the right you now have $2/3-\varepsilon$.
Next, divide the right part into two for the first approximation of $d_r$ (by taking the right side of the paper to your first pinch; again, just a pinch). This gives you $d_r=1/3-\varepsilon/2$, thus, a better approximation!
Now, repeat this procedure on the left. On the left part you now have $2/3+\varepsilon/2$. Take the left side of the paper to the second pinch to obtain a second approximation of $d_l = 1/3+\varepsilon/4$. Note that, after two pinches, you have reduced your initial error to a quarter!
If your initial guess was accurate enough, you will not need to continue more. But, if you need more precission, you just have to repeat the process a couple of times more. For instance, an initial error of $\varepsilon=1$cm reduces to less than 1mm (0.0625mm) after repeating the iteration twice.
