You don't need to set up the tool table to use comp, but you can if you like. There are two ways to use it. (Actually 3)
1) Call comp and specify the tool radius using the P word. For a 1/8" diameter bit, you'd use G41 P0.0625 or G42 P0.0625.
2) Call comp and specify the tool # in the tool table using the D word. This will use the radius of the tool in the table. To use comp with tool #3, use G41 D3 or G42 D3.
3) Basically the same as #2, but don't call any tool at all. Mach3 will use the diameter of the current tool (based on the diameter in the tool table). Just use G41 or G42.
To use comp properly, you need a lead in move where the comp is applied. Without comp, the center of the tool follows the g-code. When you call G41/G42, comp is applied during the move from the previous location to the one following the G41/G42. I like to use G41/G42 on it's own line, but you can combine it with the leadin move. Both of these will do the same thing:
G1 X0 Y0
G42 D1
G1 X1 Y1
G1 X2 Y1
is the same as
G1 X0 Y0
G1 G42 D1 X1 Y1
G1 X2 Y1
Once comp is applied, it remains in effect until you call G40. Depending on the move following the G40, comp can be either gradually or abruptly removed. You can use a leadout move, or you can raise the tool above the work and then remove the comp.
Left(G41) or right (G42) is pretty easy to figure out. Imagine walking along the toolpath in the cut direction. G42 will move the tool to the right side of the path, G41 will move it to the left side of the path. If you have a circular CCW toolpath, G42 will cut outside the toolpath, G41 will cut inside the toolpath. One thing that can be tricky is climb vs conventional cutting. Which method you're using will dictate whether you need G41/G42, as it determines the direction of the toolpath. The circular example above is using conventional cutting
Here's a little sample program that will show you how it works.
G40
M3
G0 Z0.1250
G0 X1.4629 Y1.2013 Z0.1250
G1 X1.4629 Y1.2013 Z0.0000 F25
G42P0.25
G1 X2.6956 Y2.0815 Z-0.2500 F50
G1 X8.2664 Y2.0815 Z-0.2500
G1 X8.2664 Y6.2744 Z-0.2500
G1 X3.4479 Y6.2744 Z-0.2500
G1 X3.4479 Y1.5214 Z-0.2500
G40
G1 X2.8556 Y0.9132 Z-0.2500
G0 X2.8556 Y0.9132 Z0.1250
G0 X0 Y0
M5
M30