Reserving Fuji Hakone Pass in advance

I'm planning to buy the Fuji Hakone Pass operated by Odakyu and I was wondering how I go about purchasing the tickets. Can I buy them online beforehand using my credit card? Or can I buy it the day of travel at Shinjuku station?

Thanks in advance.

You can buy them beforehand or on the day of travel. At the "Odakyu Sightseeing Service Center" in Shinjuku Station you can pay with credit cards:
http://www.odakyu.jp/english/center/index.html

One more question: when I buy the passes, do I have to start using the pass on that day or can I use it anytime? I won't be needing the pass for 3 consecutive days but I would like to be able to choose which day I wish to do go, depending on a couple of factors (weather, sky conditions, etc.)

do I have to start using the pass on that day or can I use it anytime?

You can start using it on a later day. You don't have to start using it on the day of purchase.