Ah - Japanese numbers - they drive me crazy! Given that there is no rhyme or reason, you just have to doggedly memorise them, much like we learned our times tables (or at least we did when I went to school). Be sure and nail the correct way to count people, particular one person and two people (ひとり　　　ふたり）.Be careful of 4, 7 and sometimes 9 as they change form depending on what you are counting. Just accept that they are, shall we say, idiosyncratic and drill yourself on them until remembering them isn't such a struggle. When I am talking to one of my language partners and come to something where I need a number, they always sit patiently with a small smile while I struggle to dredge up the right form, then either applaud energetically when I get it right, or gently correct me when I get it wrong.

Learn the kunyomi, learn the onyomi, be aware that onyomi with "shi" (death) are considered unlucky so kunyomi are used instead. Learn the phonetic rules how sounds change in compounds. Then learn the cardinal numbers (hitotsu, futatsu, ...). Then learn the counter words. http://www.guidetojapanese.org/learn/grammar/numbers

Do you mean number system as in the digits? Or do you mean like memorizing all of the number indicators? e.g. 三年(san-nen=three years) 一歳(ichi-sai=one year old) ... I actually don't remember too many of those myself. I'd suggest looking to see if there's an Anki program for memorizing these.

I'm about to start on this my self. The big issue is it seems the main numbers jump between kun readings and on readings even when using the same counter for example. 一人 is hitori 二人 is futari, but then 三人 is sannin. Quite confusing, but that is the fun part of learning languages ^^

I have forgotten the japanese numbers so i guess my way of learning wasn't the best ;)