My father installed a laminate floor in my living room and dining room in July 08. Although he does not do this as a profession he has done it before I had confidence in his skills. He left 1/2 gap the whole way around between the floor and the baseboard (we decided to install the floor after the baseboard was in). To cover the gap we purchased 3/4" quarter round moulding. I Started to install this moulding myself. I measured and cut, but did not nail any pieces in. Every home improvement project I do takes many months so...when I went back to work on the moulding again, I found that the entire floor had shifted. Where I once had 1/2" gap I now have 1 and 1/8 inch gap. On the other side of the room I have only 3/8" gap. If we can manage to shift the floor back is there any way to prevent it from shifting again? Any suggestions and help, of course, will be appreciated.

If the floor is a pre engineered floor and it's a floating floor the "1/2" gap this must be allowed to expand and contract. The ideal way would have been to remove the 3/4 base board and the 1/2 gap would have been there.
I will admit your floor did move a lot in one direction. To fix this is a good way but a hard way. Pop off the baseboard and see if you can slide the floor to the recommended 1/2 away from one wall. Now add a skinny piece of flooring to the big gap side. Now replace base baseboards and not tight to the floor. Then add the 3/4 round. The other approach would be to add another flat lattice 1 1/2" high by 1/2" wide and then the 3/4 on the bottom of the baseboard. With the flat build out of that strip being 3/4 above the shoe molding it actually may make the baseboard look fine and a fancier look. The floor needs to move and float. Also check the insul situation under that floor joist if its off a basement joist. The hot and cold from the basement will really keep that floor active in expansion and contraction to move the floor Hope this helped give you some options, It's a bit risky but you can tack nail the floor on the one edge to lock in that side and the movement is taken up on the opposite ends. The rick there is if the whole floor from there doesn't expand evenly to the other side it may buckle. So pick your poison.

Signed 21 Boat

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Thank you 21 Boat -- Do you think maybe the floor has shifted as much as it is going to? Maybe if we keep just the 3/8" gap on the one side we will have enough expansion room?

I don't think having 3/8 of an inch on just one side is sufficient (if tight against the wall on the other side) will give you enough expansion room. Then again, it all depends on the humidity and dryness climate you have where you live.
Here in Ontario Canada, wood shrinks in winter (due to air dryness) and expands in summer (due too high humidity), so around here, I would definitely want 1/4" minimum all around the perimeter of the room in question. Otherwise, I would definitely expect trouble down the road.

Your dad did not read the installation instructioons very closely, most every brand I have installed wants an 1/8 or 1/4" gap, never seen one calling for 1/2". Now here is a fix that will make you think I am nuts but I have done it more than once. Get several friends , wearing tennis shoes, to come over. Have them stand along the wall that now has the 1/8" gap. Everybody runs towards the 1" gap and then jump in the air and stab your feet forward when you land. This jolt will move you floating floor, it may take a couple of attempts to get it where you want it but that floor will move in whatever direction you run.