My (recycled) advice:
The best way to learn Russian cases is to learn them one at a time, otherwise you will be overwhelmed and will struggle to remember any of them. Tackle one gender, one case, one at a time. Also do singular and plural separately. If you cover too much at once, your brain will get into too much of a muddle. I suggest you get yourself a Russian grammar book, at least one, preferably several. Read the explanation of the case to get a basic understanding of how it is used. Then next comes the important bit. For each ending find some example sentences, which any good textbook should provide, I would try to find at least five, preferably more, and memorise them. I used flashcards to do this, but choose whatever method suits you best. You will need to do all of this twice, once for nouns and once for adjectives.
It will take you a while but once you've been through this process you should have a pretty good grip on the endings. It's tempting to go faster than this, out of a desire to get them all done, but you have to accept the fact it will take a while and work through it. Pretty much all the advice I've read from English speakers who've learned the Russian cases have suggested something similar: drill example sentences. You may find some of the lessons on this site useful for example sentences:
http://learnrussian.rt.com/lessons/
Any good textbook should explain when the cases are used, but whilst there are some fundamental principles that will cover most situations, the process of learning which case goes with which verbs or expressions is an ongoing process.
The good news is that you can carry on using and enjoying and learning the language whilst you're doing this. You can make plenty of mistakes with grammar and still be understood, and just the accusative case will get you quite far. It's just that cases take a bit of work and patience but you will get there.