He starts by telling the girl that she is the focus of his interest. Unlike most men, he is not actually interested in the races – he states this quite clearly in the first line, starting the poem with an emphatic non to make it clear that the races are not at all what he is interested in. What he is interested in is the girl, and so he shows her that she is far more appealing to him than the charioteers and their skill. Perhaps one could equate this nowadays to a man at a football match giving his full attention to the lady with him?
However, while he may not be interested in the races, he sees that the girl is, and so he tells her that he wants the charioteer that she supports (and perhaps has betted on) to win; and so he pretends to share a common interest and to want what she wants (cui tamen ipsa faves, vincat ut ille, precor). Later, when her charioteer begins to lose, Ovid pretends to be sad for her and curses the charioteer for the ineptitude and cowardice which has led to his love-interest being upset (quid facis, infelix! perdis bona vota puellae.) We know he is not really upset when the charioteer begins to lose. He is there to win over the girl - his apparent interest in the race and its outcome is all a fabrication to win her over by suggesting a common interest and by seeming to be concerned about things that could potentially make her happy or sad.
Ovid shows a similar concern for the girl’s happiness and wellbeing elsewhere in the poem. For example, he apparently worries that her dress might become dusty and offers to lift up the trailing material (no doubt a convenient excuse for a much more physical interest), defends her against other spectators who are apparently encroaching on her space, asks her if she is hot and would like him to fan her, wonders if she would like to rest her legs by propping them up, suggests that she might want to bury her head in his lap when a draft threatens to dishevel her hair, and so forth. He expresses a concern for her comfort in an attempt to show that he cares about her. One might also note that all these seemingly selfless offers also allow Ovid far greater proximity to the girl.
Furthermore, Ovid flatters the girl by comparing her to mythological characters – for example, the beautiful Atalanta, a famous runner from mythology; he even goes so far as to suggest that her legs are like the goddess Diana’s and that the girl is greater than even Venus, goddess of love and beauty. His flattery also takes a more physical level – while comparing the girl to these famous icons of beauty, he often becomes distracted by the girl’s physical attributes – for example her legs which her clothing selfishly conceals according to some strong personification used by Ovid (invida vestis erat!)
His mythological exempla are particularly well-chosen; Hippodameia and Atalanta are both women who posed great challenges to the men who wanted them – Atalanta did not want a husband and any prospective suitor would have to beat her in a foot race in order to win her hand, while prospective suitors of Hippodameia would have to compete in a race that would end in their death if they lost. Both these women were apparently worthy of the effort and risk and the implication suggested by Ovid is that his girl is worthy of his efforts too (although one could note that attending a race to win over a girl and watching someone else race is hardly a similar effort to taking part in a life and death competition as both Milanion and Pelops did!). However, both women, although seemingly unattainable, were eventually won over by their suitors and Ovid implies that his girl too will be won over – so she might as well give in now!
One last nod to flattery comes in Ovid’s deference to the girl as his domina – she is his mistress and he is her slave. This is a common ploy in Roman love poetry, whereby the man professes to be so hopelessly in love with the girl, that he has lost all pride, self-interest and control. We have already seen Ovid flatter her by comparing her to great figures of beauty, express common interests and claim to be concerned about her comfort – all this is apparently because he is in thrall to her – what girl could resist the charms of Ovid!
And does all this work? Well, apparently so; at the end of the poem, the girl smiles at Ovid (risit) - this is the same girl who tried to wriggle away from him earlier in the poem (quid refugis?) and Ovid ends the poem by telling his reader that's all he is going to say or do at this venue - the rest will have to happen elsewhere (hoc satis est, alio cetera redde loco) and so we can assume that he has been successful.