Hi wtid,
most verbs take the accusative case and only a few the dative. I really don't know if those have any recognizable specifics to identify them. When children learn the cases in school they do it by asking those questions "wen oder was" for accusative, "wem" for dative and "wessen" for genitive, but this doesn't make sense since you don't have a dative.
Is there a difference concerning the object between "The teacher praises his student" which in German takes the accusative "Der Lehrer lobt seinen Schüler" and "The son obeys his father"
which takes the dative "Der Sohn gehorcht seinem Vater"?
Hm, I don't know. Here's a list of verbs that take the dative: absagen-ich muss ihm absagen-I have to turn him down, ähneln-sie ähnelt ihrer Mutter-she resembles her mother, antworten-er antwortet dem Lehrer-he answers (to?) the teacher, begegnen, beistehen, beitreten, danken, dienen, drohen, einfallen, entgegen kommen, fehlen, folgen, gefallen, gehorchen, gehören, gelingen, genügen, glauben, gratulieren, gut tun, helfen, missfallen, sich nähern, nachlaufen, nützen, passen, passieren, platzen, raten, sich schaden, schmecken, vertrauen, verzeihen, weh tun, widersprechen, zuhören, zustimmen
Take the sentence "Peter weint" which is a complete sentence and compare it to "Peter begegnet" which is missing something. If you ask (in German) for the missing part, you ask "Wem begegnet Peter?" ihm, dem Vater, der Mutter, seiner Freundin.
I guess you have to learn it by heart which case follows a verb, because I think there are no rules.