you should be able to simply left click and hold on the next section of video and drag it till it "bumps" into the other section. Easy as pie.

you will probably notice some blue crisscross things where they bump together. That is called a transition. You can make it larger or smaller just by the amount you drag one clip on top of another. You will probably want to keep them kinda small.

if you grab the clip right at the edge and see a box with an arrow pointing both ways - you may actually be stretching the clip rather than moving it (it will bring back some of the clip you cut out). SO - grab the clip somewhere inside its region but not the edge - unless you want to stretch it out.

you can zoom into your timeline to make it easier to see what you are doing. I have a wheel on my mouse and when I click on the timeline and give it a spin it I can zoom in or out. you can use the up or down arrow as well.

one other thing to keep in mind, your race is probably 3 hours long - you will probably be looking at two DVD's if thats what you had in mind - unless you are going to put it back onto the original source (vcr or pvr?).

good luck