Children exposed early (before 3) to two languages easily become experts in both. While toddlers sometimes mix grammar and vocab between their two languages, by age 3 these mistakes are rare. Children quickly understand that each language is distinct and that the contexts they are used in is different (e.g., Spanish at home and English at school). By age 4, most bilingual children are fluent in their “at-home” language and near-fluent in their second language.
In school, bilingual children sometimes take a little longer than their peers to perfect reading and writing in both languages but they catch up quickly! This makes sense, they are often dealing with twice the amount of linguistic information. Nonetheless, there are many cognitive advantages to bilingualism.
Research shows that bilingual children focus well and can more easily overcome distractions. Additionally, these children are also able to better understand the arbitrary nature of language (i.e., that words are simply symbols used to describe ideas) allowing them to be more cognitively flexible in their learning.
As we know, most languages do not translate perfectly word for word. This means that bilinguals are constantly engaging with the nuance, subtlety and perspective of words and their meaning.
Does this mean you should teach your child a second language? Well, it depends. If you yourself are fluent/proficient in a second language, absolutely! Talk to them in both languages as naturally as you would in one. If your child has other people in their lives that speak a different language (e.g., grandparents or a nanny) encourage them to use their language with your child as well.
However, if you are monolingual then the cost of making the effort to learn a language in order to teach your child is likely too high. You would be better off engaging in different cognitively challenging and exciting activities. Language is just one of these activities - there are so many ways for a child to excel & grow.
References: Lanza 1992; Reich 1986; Bialystok & Craik, 2007