I am not the ideal person to help you, but I do have some questions, can I ask them anyhow?
First of all, generally buying single stocks is not a good idea. Eventually every company disappears, it might take a couple of centuries, but sooner of later most end up closing the books. If you bought individual stocks in a company that goes bust (think Lehman Brothers) they are worth nothing. This is a high risk and generally not advisable for individual investors, certainly not beginners.
In which country are you currently? Looking into how things are taxed/what costs there are is a good starting point especially if you want to get serious about them. In Belgium for example some things are tax deductible, which is especially interesting seen our tax system.
If you want to try it out just for fun, I would start by contacting your bank to be honest, to get some information and advice. I am not saying sign paperwork, but it is a relative easy to get some information, though some checking might be necessary. I also believe that Vanguard (which is hugely reputable in the USA) has a European counterpart.