Ribosomes read mRNA. Then do they "summon" a tRNA carrying the right amino acid? ?

An important aspect you are missing here is the presence of Elongation Factor Thermo Unstable... also known as Ef-Tu.

This mediates the entry of amionacyl (charged) tRNA into a free site of the ribosome (Acceptor Site). This aids in bringing the 'correct' amino acid.

Binding:     tRNA-EFtu-GTP

If the codon-anticodon pairng is correct, Ef-tu will hydrolyze that GTP into GDP + Pi... this causes a conformational change and the dissociation from the tRNA molecule allowing it to fully enter the A site. Peptide formation is now possible, and this continues until all then amino acids are aligned to form the resulting protein.