So I'm going through Nakamura right now and I ran into this sentence:

"Oni tiel malhelpis al mi, ke mi malbonigis mian tutan laboron."

I don't understand why "al" is there. It seems to me like it should be, "Oni tiel malhelpis min. . ."

For that matter, it seems that "al" is often paired up with verbs in situations where I don't understand the logic of it. Sometimes I get it, such as when paired with "diri." But often times it just feels random.

Is there a rule here?

Well, according PIV the verb "helpi" has two case governments, one with a direct object, one with the preposition "al", i.e. "helpi iun" or "helpi al iu".

The preposition "al" has a lot of use cases (PIV lists ten main ones plus some subcases), but the general sense is "to, towards something or someone". You can understand this in a concrete way, for instance "sendi leteron al mi", where the preposition concretely marks the receiver of the object.

There is also a more shifted use, as a recipient or beneficiary of an action. Some languages have a special case to mark a recipient, like the dative case in German, [de] "Ich gab dem Mann das Buch", while others use the same case as is used for a concrete movement, like Finnish uses the allative case which besides for "onto" is also used to mark the recipient of an action, [fi] "Annoin miehelle kirjan". Slavic languages like Russian and Polish have the dative case as does Yiddish, so Zamenhof was very aware of it, but he opted for the preposition "al" (which IMHO was a good choice).

Note, that while the preposition "en" + acc. means in a concrete way "into (inside)" and "ĉe" + acc. "(into) next, close" (at a hand's distance), "al" is more vague. For instance "Mi iris al la domo" can mean that after the action I was some in the vicinity of the house, perhaps even in, but that is not sure.

When it comes to a specific verb, like "helpi" here, I say it is more a personal preference which case government to use. Personally I would choose "helpi iun".

Two verbs you often see "al" paired with, as you put it, are "plaĉi" and "dolori". Because of French(?) influence liking is expressed by "tio plaĉas al mi", that pleases me. This was especially during the early years. Nowadays the construcion "mi ŝatas tion" is more commonplace (note, the original meaning of "ŝati" got shifted in this process), but you see both.

The preposition "al" with the verb "dolori" is very common. The Romance language (Spanish, French here?) influenced expression "La kruro doloras al mi" gets literally translated as "the leg gives hurt to me" or something like that. I automatically say "Mia kruro doloras".

Thanks for the explanation. BRB gotta go look up "case government."

I wish I could think of some of the more perplexing times where I saw "al" paired with a verb and just didn't get it.

Sometimes it seems obvious, such as in the example of, "Mi donos al vi libron." I mean, in this case I can literally see in my head the book physically passing from one person toward another. Or in the case of "diri," it's almost as if I can see the soundwaves physically moving in the direction of the listener during speech (and in English we might say, "He said TO me. . .").

But in other instances the reasoning is not so obvious.

At least to me has been and still is perplexing that use of "al" with "dolori", e.g. "La kruro doloras al mi". As if there would exist an abstract pain in a detached limb (imagine a Napoleonic era field hospital with a pile of amputated legs) and then this leg with pain is given to me. I think I never will get used to that idea.