I found one outlet in the kitchen that is a 3-prong

That doesn't necessarily mean that there is actually a ground wire. It could either be a GFCI outlet (which is allowed to not have a ground even though it's 3-prong) or somebody in the past could have switched out a 2-prong for a 3-prong just because they wanted to be able to plug things in and they didn't care that they created an unsafe environment.

including ideas so I don't get electrocuted

Do everything with the power off. Read a lot of books (or websites) before attempting anything if you don't know what you're doing. I've heard that the book Wiring Simplified is a good starting point.

so I don't get in trouble with the law

Pull permits. You probably can't just replace the current wiring. You'll have to make sure that all of the required circuits that the current code requires exist. For instance, kitchen counter tops require 2 20amp circuits. Your house probably only has one 15A circuit for the counter top and it might even be shared with other areas of your house which isn't allowed now. So if you are upgrading, you can't just replace the current wiring with new wiring. You'll have to add more circuits and possibly more outlets.

If you are just adding a ground wire to the existing wiring (as opposed to replacing the existing wiring with new cable), it may be a different situation.

where I might buy supplies

Home Depot?

I could probably do the hard part myself

If you plan on doing some of the work (pull wires) and then getting an electrician to do the rest (hook things up), good luck finding someone who will do that. If an electrician is doing the work, he's responsible for EVERYTHING, so he's not going to want to take responsibility for your work. You'll either have to do everything or let the electrician do everything.

Unless you mean you'll get the electrician to install a new breaker panel and then you'll do all of the rest of the wiring. Then it's two distinct, separate jobs. The electrician will do his thing, get it inspected and paid, and then move on with his life without a care about what you do after that.

The house has a circuit breaker box, has six wall switches, five overhead ceiling lights, one wall mounted light, nine wall outlets, cinder block walls. The house has been lived in for over 50 years and there's never been a problem.

Are there any insurance companies that will insure it? I want to rent it out.

This isn't really an electrical question. Seems like a renting and insurance question. Maybe call some insurance companies and ask.

Why don't you have some licensed electricians come out and tell you what needs to be done? Swapping out a 3 prong for a 2 prong outlet is fairly simple (it took an electrician maybe 5-10 min/each in my house, I think he attached the ground wire to the box itself), but you first need to be sure that the house itself is grounded and the wiring is safe. Only an electrician can tell you that.

Swapping out a 3 prong for a 2 prong outlet is fairly simple (it took an electrician maybe 5-10 min/each in my house, I think he attached the ground wire to the box itself

This would only be ok if there was armored cable to the panel and the panel was grounded correctly. Most cases will require a new wire to be run, which he probably will have to do anyhow to upgrade to 20A and have two circuits for outlets.

There is a lot for you to learn and a few new tools to get to do it right, hopefully you have a fast learning curve, if not you should hire out.

Vith, thanks for that information. The wiring for the outlets that were replaced in my house is armored cable, which explains why the electrician did it that way. My main point though is that an electrician should be able to look at the OP's house, quickly tell him what needs to be done, and what the cost will be. Getting a quote is free and gives you information about the type of work that needs to be done. There may be other problems of which the OP is unaware, that an electrician would spot and include in his quote.