using a credit or debit card?

is it safe to use a credit or debit card online? if you give your account number to someone online for a puchase, cant they use your number again, if they wanted too??(without your permission) how can you make sure this doesnt happen? i recently bought something online,(a sample ) & the person said they were going to bill my card again for the intire purchase, but i wrote & told them i wasnt interested in that, now im worried....what should i do........