Ameritrade is fine to do stock trading , go online and sign in. It will explain your eligibility to open an account or not.

Once you open account, Money should be transferred to Ameritrade account. You can do this either wire transfer (26 dollars ) or  ach transfer which will take couple days (  money , couple cents, are transferred from Ameritrade account to your checking account and later that money goes back to their account). Once the verification is completed, you have to transfer money to ameritrade and once you have balance, you will start trading.

There are different ways to trade, any confusion always call customer - care and they will help you to understand. As for example,  do you want to set a price to buy or want to buy at the end of trading day price?