Actually, 'й' can be used as 'and' as well. So, it's 4 in total: і, й, та, а
і and й - are translated as 'and' and change between each other depending on which letters surround them (we use 'й' if next word begins with vowel and use 'і' between words that end and begin with consonants). For example: мир і спокій and Олена й Ірина
та - can be used as 'and' and as 'but'. Normally, it is used interchangeably with 'і' or in a sentences where 'і' has already been used as a conjunction and you want to avoid repetition. For example: Львів і Київ, Одеса та Вінниця
a - this one can be used in meaning of 'and' in sentences where you oppose something or someone against something or someone. By its meaning also close to 'but' in some cases. For example: Він йде, а я біжу.
I hope this helps.