Can I replace my ungrounded / two prong outlets, or should I have a professional do this type of a thing?
I feel like I have seen this question asked before, but I can not find it. So I will go ahead and answer.

If you have never done electrical work before, I would not recommend this to be the project that you start on. In order to do this properly, you will need to run new wire to every outlet to add the ground line. This in itself can be a difficult task if you have never run cables through walls before. The next difficult part is connecting the ground properly. More then likely you will need to do substantial work in your breaker box and might even need to replace the whole box. In most places, you have to have an electrician come out to replace the box as it requires removing the meter while you are working.

So with all of that said, just hire someone to do it. Your home insurance will thank you for not doing it yourself.