The benefits of studying a language from a very young age are much exaggerated, and a three year old child is unlikely to learn as much as a teenager if they just study an hour or two a week. Even in the area of pronunciation, which is often mentioned as a language learning strength of young children, they are unlikely to get a good English accent while they still can't make all the sounds of their own language!
Having said all that, English classes for 3 to 7 year olds are usually fun, and those positive associations with the language do seem to have some lasting effects. If you can find a school that teaches your child some language in a way they like while also working on more important things like motor skills and socialisation (see below), there are certainly no disadvantages to starting young. This article will give some tips if you want to find the right school for kids at this young age. After reading this, you should know the things to look out for in a demonstration lesson or ask the school management or teacher about.
Immersion
The main reason people think that it is a good idea to start English as young as possible is that they have experienced or heard about five year old children who are totally bilingual a short time after arriving in the US, and while their parents are still struggling to fill in a bank application form or ask the way to the post office. Whilst part of that effect is due to the five year old child not needing as much language (e.g. banking and directions language), pre-teen children do seem to have an advantage in this kind of total immersion situation, and that can be partially reproduced by children attending a kindergarten in their own country that has an English-only policy.
Many parents, however, cannot afford an English-medium kindergarten, don't have a good one in their area, or have understandable fears about their child not learning their own language and culture. While very young students will learn little and forget quickly if they only learn for an hour or two a week, teachers can improve things by partially reproducing immersion techniques. Perhaps the most important thing is that the class should be overwhelmingly or totally in English. There are arguments for doing complex grammar or vocabulary explanations and classroom instructions in people's first languages in some classes, but a kindergarten class shouldn't anyway have grammar explanations and complex activities. Instead, all classroom instructions should be in English, because students will learn more from those real life interactions than they will from more language-focussed activities. In such a situation, students will naturally start using English to talk about classroom objects and activities with the teacher and eventually the other students, usually without needing to have an English-only policy for the kids.
Another way in which teachers can try to reproduce the best immersion conditions is to base the classes more on content and activities than on language. That means students should spend most of the class doing activities and using stories and songs that they would enjoy in their own language, but doing it in English instead. The rest of the class could have some vocabulary learning games, but there is little need for specific grammar points or drilling with very young learners.
Resources
As I said above, a good school for very young learners should base their syllabus on stories, songs, games, toys and crafts. This means you can often look around the school and judge it straightaway from its collection of books, CDs, craft materials, etc. There should also be furniture that is age appropriate, colourful walls, lots of flashcards and plastic toys for vocabulary and games, and a free lending library.
One thing parents often judge a school on is the craftwork by children on the walls. While it is good for children to be doing these kinds of things in English class, it is difficult to judge the quality of the language learning from the prettiness of the wall displays, especially if the children cannot write yet. If you get the chance to see the class doing some craftwork, make sure that all the teacher's instructions are in English, that the children are actually listening rather than just getting on with it, and that the children can do simple things like ask for things in English.
Main aims and policies
As I said above, the focus of the school should be on natural language learning through interesting games, stories, songs and crafts. The teacher should stick to English, but the children should only be forced to use English if it is part of the activity or something they have practised many times before. At least as important as these policies on the language, however, is the school's ideas on how to teach the children the good manners, socialisation skills, hand eye coordination etc that are much more important than English at this stage in their lives. These things should be clearly mentioned in the school's policies, and even listed in the syllabus.
It is not at all clear whether children at this age should be studying phonics (how to read in English) or not. Many people think there is no point doing it before they can read in their own language, as it will be much easier after. It will also take up a lot less time when they are six or seven years old, and spending time on teaching reading and writing might take some of the fun out of the lessons. On the other hand, if kids are ever going to get the kind of immersion in the language that they will really get the most from, most of that will have to be reading outside the classroom. Personally, I wouldn't let the policy on learning the alphabet etc affect my choice of school one way or the other.
The teachers
The main argument for having a specialist English teacher with this age of students is that very young children tend to learn quicker if they can associate a particular language with a particular person, just as most bilingual kids learn quicker if each parent sticks to just one language. Many schools choose a "native English speaker" for this role, but unless your child is studying many hours and so you expect them to develop a perfect British or American accent, other factors are probably more important. The first thing is the teacher being able to understand the children's first language. As I mentioned above, a natural way of teaching languages is to allow some responses from students in L1. The teacher should obviously at least be able to understand those responses from the kids. If there are no other teachers nearby, e.g. an assistant who speaks the students' language, the teacher should also be capable of switching to the kids' own language when the children are upset or really misbehaving, for example if there is dangerous behaviour.
It is equally important to have teachers with young learner training and experience. Especially if the teacher is teaching on their own and has the kids for many hours each week, they really should have the standard qualifications for teaching pre-school children and at least two years of full-time teaching experience with children that age. The next best thing is probably a trained state school primary school teacher, e.g. PGCE if they come from the UK. Teaching non-native English speaking kids is quite different, however, and so even state school teachers from English speaking countries should also have ESOL (English for Speakers of Other Languages) or EFL (English as a Foreign Language) training and experience. The best is probably the Cambridge CELTA (Certificate in English Language Teaching to Adults) with the two week extension course about young learners (CELTYL Extension), but this is quite rare. It is difficult to judge the many other qualifications that are available, but a school that lists relevant qualifications and experience of their teachers is probably a good sign. Such qualifications should be specific to working with young children and/ or teaching English to second language learners. Details of training that the school gives its teachers could also be relevant.
Before hiring full-time teachers, all schools should ask for a criminal record check in that person's country, so please look for mention of this on the schools website or in its brochure.
Marketing
As I said above, there are many things that are more important than being a native speaker when it comes to teaching the numbers 1 to 10 to little kids and making it fun. Schools which spend a lot of time telling you which countries their teachers come from and not much time telling you about their methodology, qualifications and experience are usually best to avoid. Studying English at university or going to a good university are also fairly irrelevant.
Another bad sign is a school that makes overambitious claims about what your young child can learn and how fast they can learn it, especially about how fast they will learn to speak and how good their pronunciation will be. In fact, the natural learning techniques that I mentioned above expect children's speaking to lag far behind their comprehension, just as it would in L1.
Lots of language learning jargon and mention of language learning experts' names (Pinker, Krashen, Chomsky, etc) is usually a bad sign.