Both is only used when you have two options. Ex; I'll have both the spaghetti and the pizza, please. You can think of "also" like a + sign. Whenever you're adding something to your conversation you might use it. Ex: I will have pizza. I will also have spaghetti. ("spaghetti" was added to pizza) Jack will go to Italy. I will also go to Italy. ("I" was added to Jack) "Too" can be used similarly to how "also" is used, but it goes at the end of the sentence. I will have pizza. I will have spaghetti too. Jack will go to Italy. I will go to Italy too.

'Too' and 'also' have the same meaning. There is no difference in level of formality. The difference between 'too' and 'also' is to do with where the word goes in the sentence. You can put 'also' in the middle or at the end of a sentence, depending on what it refers to (which word is the extra element). 'Too' can only go at the end of the sentence. She speaks Spanish, and she also speaks French. She speaks Spanish and she speaks French, too. Those two sentences have the same meaning. The only difference is the word order. The word 'both' means 'the two' . She speaks both French and Spanish. In this sentence the object is 'both French and Spanish'.

Both is two things only. Too and also are basically interchangeable, but they each have specific usages that sound better to a native's ear. It is very subtle. I am not even sure I could teach you how to know when. Just remember that too is more informal and also is more formal.