How does high-fidelity of DNA replication depend on the formation of hydrogen bonds?
DNA polymerase must catalyse the addition of 4 different nucleotides to the growing strand. This means that it cannot directly determine which base to incorporate at a specific point (how would it 'know' which base to incorporate and how it would it change its specificity for different bases). This means that the specificity for which base pair to incorporate is dependent on the template DNA strand.

Correct Watson-Crick base pairing (that is, hydrogen bonding) between the template strand and the nucleotide to be incorporated triggers the closing of the finger domain of DNAP around the primer-template junction and positions the latter in the optimal position for catalysis (with the $\ce{\alpha-PO_4}$ of the incoming nucleotide near the $\ce{3'-OH}$ of the primer for a nucleophilic attack catalysed by two $\ce{Mg^{2+}}$ ions). This is where the conserved tyrosine residue you mentioned comes into play. An incorrectly paired nucleotide will not trigger this conformational change and will not be positioned optimally, thus catalysis is less likely.

Furthermore, the DNA polymerase makes contacts with the minor groove of the primer-template junction through hydrogen bonds. This interaction is not base-specific (all Watson-Crick base pairs have he same pattern of hydrogen-bond acceptors in the minor groove) but only occurs when the correct nucleotide is incorporated, thus stabilising the complex. 

Finally, discrimination between ribonucleotides and deoxyribonucleotides is done by steric exclusion of the $\ce{2'-OH}$ by amino acid residues in the binding pocket.

These factors can be thought of as kinetic proofreading as they simply slow down the reaction rate and provide time for an incorrectly paired nucleotide to dissociate. However, they can still be incorporated and many DNA polymerases have a $\ce{3'-&gt;5'}$ proofreading exonuclease that can remove incorrectly paired nucleotides. This proofreading is again mediated by interactions between the DNAP and the primer-template junction (ie hydrogen bonding with the minor groove). A weakened interaction due to an incorrectly paired base reduces the affinity between DNA and the catalytic site and increases the affinity between DNA and the proofreading site (because it has a preference for cleaving ssDNA from the 3' end).