When it comes to RAM, ignorance is bliss.
I wish I didn't know about RAM, tbh.
That being said, it is good that you are getting 4 x 1GB of the exact same kind.
Many problems can happen with RAM in general, even if you do everything right, but many MORE problems can happen if you do things in a way that isn't ideal.
That being said, you probably don't want to put the sticks in 1 at a time. I think that will just quadruple your pain from the whole process.
Obviously, you can't physically stick all 4 in at the same time, but if I were you I would do it all in one "shot" without turning the computer on between inserts.
There are a couple different ways to approach this process, but the one that I think causes the least pain is to follow the below steps in the exact order they are in.
1) Pull the cord out of the back of the computer so the computer is not connected to a wall outlet
2) Hold in the power button for 1 minute to try and be sure all the power is out of the computer
3) Crack open the case. When you are doing this, make sure you touch the metal part of the case to discharge any static electricity in your body harmlessly on the case metal.
4) Find the battery, it looks almost like a quarter and it will probably be close to the video card. Look at how the battery is oriented in the slot.
5) Using a flat screwdriver, gently push on the metal piece at the back of the slot that is holding the battery in the slot. This should pop it out of the socket. It will probably be forcefully ejected so it may end up anywhere.
6) Grab it by the sides and set it down on a non conductive surface like wood with the smooth side that has letters and numbers down and the side with crisscross markings up. Try not to touch the side that will be up if possible.
7) Look at the clock and note what time it is.
8) Take out all of the RAM sticks that are in the motherboard currently.
9) Put in all the RAM sticks that you want to have in there. I generally go from left to right myself. Once you are sure you have the RAM oriented correctly so that it will go into the slot (its keyed so it won't go in backwards) then push firmly and hard. There should be a slight snap as the devices on the sides lock into the sides of the RAM. If you don't hear this or if you have to close these yourself, it probably isn't pushed all the way in and it will probably not boot for that reason.
10) Sit there and wait.
11) When you are 15 minutes forward from the time you looked at the clock, then take the battery and stick it back in. It should be oriented similarly to how it was the first time if possible. It shouldn't matter much how it is oriented as long as the right side is up and the right side is down, but it doesn't hurt to try to restore it to how it previously was if you can.
12) Close the case
13) Put the power cable back in between the wall and the PSU.
14) Turn the computer on
If you are religious, somewhere between 13 and 14 it wouldn't be a bad time to pray.
If you do all of these things this way, it is maximally likely to work right the first time and save you a lot of time and effort trying to resolve RAM problems which can be among the most frustrating things to try to resolve.
There is no guarantee this will work the first time, though.
As mentioned before, RAM is... finicky. Sometimes it doesn't work temporarily for no rhyme or reason that most people can tell. Then you repeat the same thing you already did and it starts working.
The 4 most important pieces of that process are probably the battery being out 15 min, all the RAM going in the board in the same shot, pushing the RAM hard to make sure it is all the way in, and not having the PSU cable attached when you do this.
If you have to repeat steps because it doesn't work, those are the ones you are probably going to want to repeat. Not necessarily in that order, always remove the PSU cable first before you do anything else.
If you do have problems, try just starting all the way over again and repeating the steps again just like they are shown. You should have no problems doing this 3 times in a little over an hour if necessary.
Sometimes it just takes a bunch of repetitions of this for something to "click" inside the computer and to have things working, so don't be worried if it takes a couple times.
If you do it 4 or 5 times and it still doesn't work, then come back in here and we can try to see what is going on with it from there.