What are the explanations of the Vav of Veahavta in the Shema as it comes to add something?
The Sforno seems to say that the vav "you will then enjoy doing things which are pleasing to Him when you understand that there is nothing in this world which is more worth doing."
The kitzur Bal Haturim says that the vav is necessary so that the word v'ahavta has the same letters as "ha'avot" (the forefathers) so it can invoke them and their lives.
The Ohr Hachaim writes
The conjunctive letter ו means that not only is there a commandment to accept the authority of the Kingdom of G'd but there is an additional commandment to love G'd. The sequence of the verses also teaches that we must not make the mistake of believing that love of G'd is possible without an initial dose of fear of the Lord. The Zohar volume three page 56 spells this out. The letter ו then means that after we have achieved a degree of fear of the Lord we will be able to develop love for Him. The reason the Torah uses the word את which implies joining something, is to teach us that the means to develop דבקות ה׳, an affinity for G'd, is by loving G'd in addition to fearing Him.
I am no expert on biblical grammar but on a simpler level, there is a notion of a vav hahipuch (according to some) which changes the tense of a word -- here, Ahavta, a past tense verb is changed to the future (and you shall love).
This is called vav hahipuch or the "reversing" vav. It is a common Biblical technique to add a vav at the beginning of a verb. The reversal changes a past tense verb into the future and a future tense verb to the past.
In this case, the verb ahavta would mean "you loved". Having the vav in front makes the term mean "You shall love", meaning the future tense.
I'm not sure why the Bible uses this technique. That's probably worth asking a separate question.