How can I convert 4 ft fluorescent tube fixture to be used as a plug in fixtures?
You have the right idea, but some of your terminology is wrong.

In general, ALL household electrical work involves connecting the various lights, heaters, motors, computers, etc. all together with black to black, white to white, ground to ground.

This kind of a connection is called PARALLEL (not series).  

To be specific, each of your lights will have a black wire and a white wire (and probably a green ground screw).

Your plug-in cord should also have a black wire and a white wire and a green (ground) wire.

To make it work electrically, you want to connect all 4 of the light's black wires together, and hook them to the black wire of the plug-in cord. You could use a really BIG wire nut to hook these 5 black wires together.

You also want to hook all 4 of the light's white wires together and to the white wire of the cord. BIG wire nut number 2.

You also want a ground wire from the green housing screw on each light coming all together electrically, and connected to the green ground wire of the plug-in cord. Big wire nut number 3.

Now, the best way to go about making those many connections can be as much art and skill as it is science.  Depending upon how the lights will be arranged, you might find it better to do something like the following...
1) at light 1 you have just the cord coming in, and the white black and ground of light 1, and an "extra" wire that will go off to light 2.  Hook all 3 blacks together; hook all 3 whites together, hook all 3 grounds together.
2) at light 2 you have the "extra" wire from light 1 coming in, the black/white/ground from light 2, and another "extra" wire that will be going over to light 3...  again, all 3 blacks together, all 3 whites together, all 3 grounds together...
and so on down the line.

This kind of a connection is called a "daisy chain parallel connection".  It is electrically the same as if you put all 5 black wires into a single BIG wire nut, and similarly with whites and grounds.  Since you probably don't want all 4 lights stacked tightly against each other though, it might be much more practical.

Even though you have the juice going from one light to the next to the next...if you draw it out on paper you will see that since all of the blacks are tied together and all of the whites are tied together...the juice is actually not flowing electrically THROUGH one light and into the to the next.  Electrically, you could draw ALL of those black wires as one big dot in your diagram.  Since the black wires are all hooked together somewhere, then as far as the electrons are concerned, they are all hooked together...period.

If it helps you to visualize it, draw it first like the BIG wire nut example at the beginning of this post.  Then draw it again but take that one BIG black wire nut and draw it as 4 smaller wire nuts right next to each other, with tiny little connections between them.  Your one BIG wire nut has changed into 4 smaller ones, but those 4 small ones are all hooked to each other.  Can you see how that is electrically the same?  Do the same with the BIG white wire nut and the same with the grounds.  Now just keep spreading them further apart in your drawing until they are spread out the way the lights will really be arranged in the room.

Or another way to look at it is...each light has a black/white/ground.  If when you're done, each of those black wires can "find its way back to the black of the plug-in cord" (doesn't matter how it gets there as long as it's always black); then you're golden.  Obviously, same for the whites and same for the grounds.