All the information on how to operate a mobile service with Boost is contained in the User Guide which comes with the Boost Starter Kit.
But in short, the two ways of checking your balance are...
#111# [SEND] on your handset. This is the USSD service which allows you to check remaining data, expiry date, details on your offer, recent history and of course to recharge.
The other method (also on the handset) is the following website, http://care.boost.com.au this will only work on your Boost Pre-Paid service. This supplies the same information and includes the same features as the USSD service.
It may be 2015, but the two offers that Boost have, UNLTD and ULTRA are quite simple and really don't need the extra bells and whistles. Afterall we don't really need to complicate things for the sake of having features/components on a website for instance, when they're not necessary.
Apart from having a longer list of past transactions (in which case you'd have to suggest going to a post paid service provider and pay extra for that feature), I'd say Boost fits the bill for the majority of the company's prepaid customers.
CORY | I do not work for Boost or Telstra.
Boost Care: 125 8881 or 1800 026 678 . Or Live Chat 24x7: http://livechat.boost.com.au