Unfortunately, there's no short answer to this question. In a lot of verbs, you'll find that English and Russian agree on an accusative (direct) object, and even on a dative (indirect) object. The latter are obviously verbs of giving, sending, transferring, etc. and won't be difficult to spot.
However, in other verbs, the case of the complement has to be learned. For instance, the verb помочь (help) takes a dative object in Russian (as in German), but an accusative one in English: Я могу помочь тебе с этим. I can help you with this. Interestingly, учить (to teach) takes an accusative student and a dative subject. Perhaps in the Russian logic, teaching is viewed as an instance of leading someone to(wards) something: Я учу его русскому языку. I'm teaching him Russian. Finally, the verb наслаждаться (to enjoy) takes an instrumental object: Наслаждайся моментом! Enjoy the moment! (Carpe diem). This all may seem random at first, but as you continue to learn verbs and read more Russian, you will develop a feel for the actions that are accomplished by means of (instrument) an object, for example, and it will make sense. I guess it helps to start thinking like a Russian.
As for sources, the dictionaries Яндекс, Abbyy Lingvo and PONS all give information on the objects and complements of verbs. Usually in the form of кого/что for accusative, кому/чему for dative, кем/чем for instrumental, etc. They also give perfective and imperfective pairs.
However my favorite conjugation website by far is Rifmovnik. You have to enter the verb, then choose СЛОВОФОРМЫ from the drop-down menu. It will conjugate one aspect, and provide a link to the conjugation of the corresponding perfective or imperfective. Additionally, you can enter any form of any part of speech and it will take you to the entire paradigm of the word in question. This is helpful when you see a conjugated or declined form, but have no idea what the citation (dictionary) form is. It also indicates stress throughout, which is invaluable.
As a course of further study, it helps immensely to have an understanding of the function and meaning of the plethora verb prefixes used in the Russian verb system. If your Russian is advanced enough, this is an extremely informative and easy to follow PDF on the subject: Изучение глагольных приставок.
Good luck and enjoy!