Learn Spanish (Latin America): Quiero mejorar mi vida.

When you use two verbs together to say you want to do something, only the first verb changes to match the person. Because we already changed the first verb to quiero (I want), the second verb mejorar stays in its original dictionary form (the infinitive). This is just like saying "to improve" in English!

Why does the verb querer change to quiero? Where does the "i" come from?

Querer is a stem-changing verb. This means the core of the word changes slightly when you use it. For querer, the first e changes to ie for most of its forms. That is why "I want" is quiero and not "quero".

Since vida is a feminine word, why do we use mi instead of a feminine word like mía?

The short word mi (my) is used for both masculine and feminine words as long as there is only one of them. You only need to add an "s" to make it mis if you are talking about multiple things. The word mía actually means "mine" rather than "my".