Most of what I know I picked up from various 2+2 threads, so I am far from expert on the subject.
The absolute basics are that you want two wallets (where bitcoin can be stored and transferred to other wallets).
One wallet should be on an exchange (for example Circle or Coinbase, where bitcoin can be exchanged for dollars and transferred to/from your bank, which can be linked the same as linking your bank to other $ wallets like payPal/Skrill/etc). The other should not be on an exchange (Electrum or blockchain, for example).
Use the exchange wallet to transfer to and from you bank and the other wallet to transfer to and from the site (apparently the exchanges sometimes take issue with transfers directly to gambling sites). Transfer between the two wallets as an intermediate step.
If you wish to take the bank out of the equation, there are some bitcoin ATMs or localbitcoins.com as alternatives.
https://bitcoin.org/