They're all two prong except a select few in the kitchen. Is this a project I could take on with NO electrical experience other than minor soldering, or is this something I should not attempt?
Question two (should I make a new "Question"?): How would I go about doing this?
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.
On the one hand you don't need to run a new circuit to replace a receptacle, on the other hand putting in a new receptacle alone does absolutely nothing to modernize your system. Millions of houses have old wiring and they are fine. The only good reason to just replace the receptacle is because it is falling apart or won't hold the plugs in anymore. The problem is all new receptacles are grounded and your wiring was done before a third ground wire was required. You are likely to either have BX spiral metal jacketed cable or knob and tube for old wire. You can tell if you look in your basement or inspect where the wire enters the inside of the box. It is most likely BX if the house was built after about 1910. if you have BX you can replace the receptacle with a grounded one that uses the metal box and metal jacket as the path to ground. You can either use a metal clip that slides onto the box or you can scrape the metal clean an put a ground screw into the box. To that you attach a bare ground wire that you connect to the ground lug on the receptacle. The existing black wire goes to the gold terminal and the white wire goes to the silver terminal. It isn't difficult, should take you less than an hour.
As to the insurance fears and all that, this is not really likely to be what's potentially dangerous about your home wiring. The main danger of old wiring is in the ceiling boxes where light fixtures are mounted. Over years and years the heat from those old hot incandescent light bulbs makes the insulation on the wires brittle, creating the potential for these slow short circuits that heat up in the box but don't quite blow the breaker or fuse. You are best advised not to mess with old fixtures. Doing things like adding a switch leg is ill advised. If you have to deal with it you can only hope that an enlightened electrician from the days of yore left you some slack. Then you can cut back the ends and get to good insulation. But that's another story.
You should be fine. As a homeowner you should develop a plan for upgrading your house over time. Avoid half measures. When you decide to rewire a section of the house disconnnect ALL the BX on a circuit and re-run it in romex.
Call a local licensed Electrician. They will be able to do it faster, safer, and possibly cheaper (if you factor in what your time is worth).
It's likely not a matter of simply replacing each receptacle with a three prong version, you're probably going to have to pull new cable. There may be permits involved, or other legal/code compliance matters that you will not be aware of.
If you live in an area covered by National Electrical Code, you may simply be able to GFCI protect the circuit. This protection can be provided via a GFCI breaker, receptacle, or standalone device.
There's a few stipulations, which are explained in greater detail in this answer. But basically it involves not connecting the ground terminal, and properly labeling everything.
More recent code changes actually allow you to use the grounding conductor of a different branch circuit, though it sounds like that might not be an option in your situation.
+1 to @kellenjb and @mcktimo, but let me just add: It's possible that the ground wires are there in the wall, and that someone put in two-prong outlets anyway. The fact that there are some 3-prong might mean that in fact there are proper ground wires. Or it might mean that someone bought a 3-prong outlet, then went to put it in, saw no ground wire, and just shrugged and connected the two wires. Or they might have run 3-wire cable to the kitchen but not the rest of the house.
If the ground wires are there, installing new outlets and hooking them up is a pretty easy job. It's not hard to check: turn off the power to an outlet at the fuse box (the first step before touching anything electrical, a rule I can attest to from too many times saying, "ah, I don't want to go all the way down the basement, I'll just be careful ..."), take the plate off an outlet, and examine the wires leading into it. If you have modern wiring, there will be a black wire, a white wire, and a bare wire. If it's older, you may still be able to count if there are 2 wires or three.
