I am curious as to the processes and mechanisms involved in the extension of pseudopodia in amoeba. How does the cell know and control the direction and extent of pseudopodia formation at a molecular level? I am not particularly interested in the taxes that amoeba recognize, but rather the mechanism of response to these taxes.
The extracellular cue signal must be relayed to the cell by Rho family of GTPases, like in the case of filopodia and lammelipodia. This causes local actin polymerization leading to extension of pseudopodium.
For a casual reference you can check the wikipedia page on Rho family of GTPases. Cell biology books like MBOTC also have information on mechanism of cytoskeletal dynamics.