All cryptocurrency transactions must be confirmed on the blockchain before credited to your balance. This is a completely automatic process and therefore there is no way to speed this up, as it is determined by the network.
Shuffle.us requires a certain number of confirmations on the network depending on the coin you choose, and this information can be seen via Transactions > Purchases.
The time this process takes is fully dependent on the state of the network as well as the fee used on the transaction (i.e. setting a higher fee will typically result in faster confirmations). Generally if the network is congested or under heavy demand then you can expect transactions to be slower than usual to confirm.