All you need is a computer, a modem and Internet access.
Most major brokerages offer online trading through their Web sites.
You simply open an account and mail in a check. Then click over to the brokerage's Web site and log on via the password they'll send you. From there you can check the status of your account or place an order. All reputable online brokerages have security measures in place. Read up on them first at the Web site or call and ask, to ease your mind.