a) Placement of adverb
The general rule, is that they come after the past participle. However, that does depend on the length of the adverb.
In simple tenses (présent, futur simple, imparfait, etc.) the adverb is always placed after the verb (regardless of length).
- Il mange beaucoup.
- Elle parle franchement.
In compound tenses (passé composé, plus-que-parfait, futur composé…), simple and short adverbs (bien, mal…), adverbs of manner and quantity (beaucoup, trop, assez…) as well as certain adverbs to do with time (souvent, toujours, trop, tard, quelque fois…) are placed between the auxiliary verb and the past participle:
- Il a beaucoup mangé.
- Nous avons bien dormi.
However, if the adverb is longer and made up of several syllables, then we place it after the past participle:
- Elle a parlé franchement.
- Ils ont travaillé sérieusement.
Adverbs which define a spatial or temporal context (hier, aujourd'hui etc.) are most often placed at the beginning or end of the sentence. Rarely are the placed in the middle and I would avoid it.
- Hier, je suis allé au magasin.
b) Adverbs in the negative
When an adverb is placed in front of the verb in an affirmative sentence, then it is generally placed after the second element of the negation (i.e. ne…pas, ne…plus etc.) in the negative.
Some notable exceptions to this include certainment, généralement, peut-être, probablement, sans doute.
- Elle n'a probablement pas mangé.
Longer adverbs like franchement maintain the same position in the affirmative as in the negative i.e. after the past participle.
- Elle n'a pas parlé franchement.
Vraiment can be placed before or after the second element of the negation but it does change the meaning of the sentence:
- Elle n'a pas vraiment parlé. (She didn't really speak. - she talked, but not about something in particular or she wasn't serious)
- Elle n'a vraiment pas parlé. (She really didn't speak. - she didn't say a single word.)
The position of the adverb here dictates which verb is being modified. That's to say in example #1 it modifies parlé, so we know that she did in fact speak, but it wasn't a lot or in depth. In example #2, the adverb is modifying the auxiliary, which indicates that the action may not have even taken place in the past at all.
This is something you will get a feel for as you hear certain adverbs being used one way or another, but there is not definitive list. Most adverb placement makes sense when you translate it back into English and if it doesn't then it's likely not correct.
I hope this helps and I hope it isn't too much at once.