פירוש על קידושין 81:3

The gemoro will learn it out [from verses].

All the more so when she is a minor if she accepted her betrothal she is betrothed. That that it taught:"youth" [is just] to let us know that preferably a minor should not be betrothed as it is explained in the gemoro.

A man can betroth a woman through an agent. This would mean that the man gives money to an agent to use in betrothing a certain woman. This probably would have been a common means of doing betrothal if the couple lived far apart from one another and was matched by others, as was nearly always the case. Similarly, a woman may appoint an agent to receive her betrothal money.

A father has the right to marry off his daughter while she is still a young girl (na’arah). This is defined as a girl between the ages of 12 and 12 1/2 who has already reached puberty. He may also marry her off at a younger age, but not when she is past that age. When marrying her off, he may use an agent to accept her betrothal money. Basically, the father takes her place in matters of betrothal.
I should note that while a father had the legal right to marry off his daughter and not his son, and this right extends only until she reaches 12 1/2, in practice the father played a very large role in arranging matches for both sons and daughters no matter what age they were when they married. The idea that a 12 1/2 year old girl became totally independent of her father was probably as strange of an idea in the mishnaic period as it would be today.