Change of form of some (Latin) prefixes like ex-, ad- into ef-, a-: are there rules or conditions?

There are many cases of prefixes changing their forms. For example

• ex- can change to ef- in front of f, e.g. effusion.

• ad- becomes a- in front of b, e.g. abate.

Are there some more general rules or a summary of such changes that can help me figure out the meanings of unfamiliar words, and recognize the prefixes in the words?

There were several stages in the history of English where prefixes took different forms, resulting in the variety we have now:

1. At some stage in (early?) Latin, prefixes often assimilated to the following consonant, acquiring e.g. a second f as in effusion. This was mainly determined by rules of pronunciation; just as we say a man but find *a apple jarring in English, so the Romans found *exfusio jarring and effusio more harmonious. We also pronounce the v in have often like an f before t/p/c: we always pronounce have to as hef to or hefta. Many other rules based on pronounceability also emerged in this stage (see below).
2. At some (later?) stage of Latin, the Romans also used unassimilated, unchanged forms at the same time, where the basic form of the prefix was used regardless of the sound that followed: you will often read e.g. both adlatus and allatus "brought to", sometimes even by the same author. Dictionaries have huge lists of entries like "adl-: see all-", because they don't want to list two forms of the same word twice.
3. In premodern French, different rules applied, and some Latin words were changed in different ways. The prefix ad- often changed into a- or à-. This could mean losing the geminated ("doubled") consonant it used to have: so Vulgar Latin abbatere (from ad- + battuere, "beat") became abattre at some point in French. English borrowed some words from French before these forms had changed, other words after.

It is hard to predict which rules will apply to which word, so you have to take all three options into consideration. A few common variations of prefixes in Latin, all mainly in stage 1:

• a/ab/abs/aps/as/au- "away from"; as a preposition a/ab/abs.

  There may not be a strict rule. Normally abs- or aps- before c, p, t; sometimes as- before p; sometimes au- before f; otherwise a- before consonants; ab- before vowels and h.

• ad/a/ab/ac/af/ag/al/an/ap/ar/as/at- (French often à/a-) "towards, in addition"; preposition ad.

  Rule: ac- before q and c; ad- before h and vowels; a- before gn, often before sp, sc, st; rarely ag- before n (usually an-); otherwise assimilated before consonants.

• ambi/amb/am/an- "both sides"; no preposition; noun ambo.

• con/co/cog/col/com/cor- "together with", as a preposition or suffix cum.

  There is no very strict rule. Often co- before vowels, g, h, and n, but not only or necessarily; rarely cog- before n (usually con-); col- before l; cor- before r; com- before b, p, m, sometimes before vowels; otherwise/usually con-.

• de- "down, away, not", preposition de.

• dis/di/dif/dir- "apart, away, not"; no preposition.

  Rule: dis- before c, p, t, s [except before sc, sp, st]; di- before sc, sp, st; assimilated dif- before f; dir- before vowels and h; di- before other consonants.

• e/ex/ef/ec- "out, away"; preposition e/ex.

  Rule: ex- before vowels and h, c, p, t; ec- or (assimilated) ef- before f; after ex-, a following -s- may be dropped (exsanguis/exanguis both exist); e- in all other cases.

• in/im/il/ir- (French often en/em-) "in, to"; preposition in.

• in/i/im/il/ir- "un-"; no preposition; related to non and other nasal negations.

  These two prefixes have the same form but a different origin. The same rule applies: il- before l; ir- before r; im- before b, p, m; i- before gn; before other letters in-.

• ob/oc/of/op/o- "in front of, blocking"; preposition ob.

  Originally op- (operio); oc- before c; of- before f; sometimes shortened to o- (omitto); otherwise ob- or sometimes op-.

• per- (French often par-) "through"; preposition per.

• por/pol- "forward"; no preposition; adverb porro.

  Rule: pol- before l; otherwise por-.

• prae- (French pré-) "front, forward"; preposition prae.

• pro/prod- "before, forward, instead"; preposition pro.

  Rule: prod- often but not always before vowels, otherwise pro-.

• re/red- (re-in- often contracted as ren- in French) "back, again, properly"; no preposition.

  Rule: red- usually before vowels and h.

• se- "apart"; no preposition.

• sub/suc/suf/sup/sur/sus- (French often sou/sous-) "below, up from below, supporting"; preposition sub.

  Originally sup; su- before sp; sus- [from subs-] sometimes before t, c, p; otherwise assimilated before c, f, p, r; otherwise sub- or sometimes sup-.

• super- (French often sur-) "over, above"; preposition super.

• trans/tran/tra- "over, beyond"; preposition trans.

  Rule: tra- often before i and consonants; tran- before s; otherwise trans-.

This is actually much simpler than one might expect, if one only paid attention to spelling.

The name of the phenomenon is Assimilation,
and it's a very natural process that occurs in every human language.

If a prefix ends in a consonant, and then is attached before some other consonant,
then the consonant at the end of the prefix is going to change in contact.

That's called assimilation; and in fact assimilation is an example of assimilation,
because assimilation comes from Latin ad 'toward' + simil 'same'; i.e, 'become similar'.

But the D at the end of ad changed to an S, making a double SS
(which was probly pronounced as a double /s/ in Latin; this happened in Latin).

In the examples above, you'll find that an underlying final consonant (say B in sub-)
will appear before vowels, but before /k/ (C in Latin) it becomes /k/ (suc-), before /p/ or /t/ it becomes /p/, before /r/ it becomes /r/, etc. There are individual rules for lots of prepositions and prefixes (which constitute the same class of morphemes, but define different uses for them).

As for a general rule, it's generally the following consonant that determines the fate of the consonant at the end of the prefix. That's because by the time you've gotten to the end of the prefix/position you know what it is and you don't need to hear the end, so you slur over it to get to the beginning of the next morpheme.

This happens all the time, I repeat. But with Latin prefixes, the assimilations were already done and fixed in place before they came to English, so they're not productive anymore and have to be learned by rote (or by learning Latin, as it used to be done).