Search the website for the closing date, if you can't find the date call or email them. Generally you can expect that the first closing date will be about a month after the account was opened, but that exact date is just a guess.
The closing date is the date each month that the statement closes. Everything you buy between those closing dates will be on one statement. When the statement closes a bill is generated and you are given several weeks to make the payment. This due date will generally be several days before the next statement closes.
If you make payments early that will reduce the amount owed when the bill is generated.
Because the limit on your card is most likely very low, you may find it advantageous to pay some or all of the balance before the statement closes, if you need more room to make a purchase. You don't want to make a purchase that will take you over the limit because it might be rejected, or the credit card issuer could hit you with a penalty for exceeding the limit. Even getting too close to the limit may limit your flexibility.
Remember that because of the grace period between the closing date and the due date, if you wait until the due date to pay the bill you will have almost two months worth of spending on the card. That means if you are using around half the limit each month you could get close to the limit without realizing it.