What _as well_, _also_ and _too_ add, and to what
As well, also, too and as well as all say that something is added, and a sentence that uses one of them is clear only when the reader can tell what is added to what. Each also has its own place and grammar: where the adverbs sit, what as well as does to the verb after it and to the order of a series, and how to word the addition so that it has one reading.
What as well, also and too mean
As and well are simple, common words that form phrases functioning as a single word, and careless writers often make mistakes with as well and as well as, some grammatical and others of meaning. As well is a multiword adverb meaning "also", which can be part of the idiom might as well, and it can also be used as an adjective in the expletive construction "It's just as well…". As well as is a multiword preposition meaning "in addition to", and it can also be a phrasal connective used in making comparisons. It is just as well means that some event or situation is fortunate, and that the likely alternative could have been worse. Saying you might as well do something means there is no reason not to do it ("While you are waiting, you might as well check your email").
Too does not always mean also: it can mean to a higher degree than desirable, permissible or possible ("Papa Bear's porridge was too hot"). Either is used after a statement that adds a negative thought to another negative thought ("He does not smoke, and he does not drink either").
Where also, as well and too sit
As well, also and too have similar meanings, and the main difference is position: also often comes before the verb ("She also speaks French"), while as well and too usually come after it ("Bring a pencil and some paper as well"; "He's smart, too"). Also at the beginning of a clause or sentence can serve as a conjunctive adverb, like moreover ("This drug is expensive. Also, it has many side effects."). Too can sometimes appear directly after the subject, and there it should be set off with commas ("I, too, have some misgivings").
As well as and the verb after it
As well as has a meaning similar to and, but it is a multiword preposition, not a conjunction. If its complement is a verb phrase, the verb in that phrase usually takes the -ing form ("The surgeon explored the abdomen, as well as removing the appendix"). If the as well as phrase links a verb phrase to an infinitive phrase, the verb should be a bare infinitive, the stem without to: "The nurse had to record his vital signs as well as give him his medication", not "as well as to give him his medication". As well as is not always a preposition: as a preposition it introduces the -ing form of the verb, or sometimes the bare infinitive, but as a phrasal connective it introduces an independent clause, with a different meaning. "She sings as well as dances" means that she sings and she dances, and "She has to sing as well as dance" that she has to sing and has to dance, while "She sings as well as she dances" means that she is just as good at singing as at dancing.
As well as and the order of what is added
As well as implies addition but is not a substitute for and: it should not be used instead of and before the last item in a series, but to add obvious information after some less obvious information has been listed: "The β-lactam antibiotics include the cephalosporins, the monobactams, the penems, and the carbapenems, as well as penicillin", not "the cephalosporins, the monobactams, the penems, the carbapenems, as well as penicillin". As well as introduces information the reader already knows or expects, after the sentence has given new or unexpected information, so it can acknowledge what readers already know or can easily guess once the sentence has pointed out something they might not expect: "The male hormone testosterone is found in women as well as in men", not "in men as well as in women".
Making clear what is added to what
Also and as well imply addition, and too can imply it as well, so a sentence that uses one of them to imply addition should make clear what is added to what: "He is having coffee, too" leaves open whether more than one person is having coffee or he is having coffee as well as something else. The same holds for as well as used to imply addition: "Lee has been married to Sam as well as Violet" leaves unclear what is added to what, while "Lee has been married to Sam as well as to Violet" and "Lee, as well as Violet, has been married to Sam" each make it clear.