How does GTP help in the step of codon recognition?
GTP based structural changes (even motor actions) are very common in biological systems. For e.g. G-proteins, Rab-GTPase (vesicular transport), Ran-GTPase (Nuclear export/import).

So all these GTP-bound proteins make use of an intrinsic or assisted GTPase activity to convert GTP to GDP. This conversion causes change in the structure of the associated protein. Going back to the GTP bound form requires proteins called GEF (Guanine nucleotide Exchange Factors).

So in the case of translation elongation, the elongation factor is a GTPase which changes confirmation upon GTP hydrolysis. This confirmational change twists the tRNA so that the bound amino acid moves closer to the peptidyl-transferase center (if P-site is in the left then the amino acid is bound to the rightward CCA tail of tRNA. The twist causes the amino acid to move leftwards- towards the P-site). 

You can refer books like Genes by Lewin for details.