Well, I'm not really sure what you need but I'll take a swing at it.
Plotting a vector is pretty easy if you keep it simple.
For Traveller you need to know the maneuver G you're applying, the duration applied (game turn), and the scale you're using. For CT the scale is 1mm (millimeter) equals 100km (kilometers) and a turn is 1,000 seconds. So 1G of thrust for 1 turn is equal to a vector of 100mm (10,000km). 2G of thrust would double that. 3G of thrust would be three times that. And so on.
To plot your movement you just add the intended thrust for the current turn to the vector of the last turn. This is done by drawing your new thrust vector (a vector is a line with an origin point, and a terminator generally represented by an arrowhead) on the terminator of the previous one, and then connecting the origin of the previous vector to the terminator of the current vector to get the new vector.
For (simple) example. A ship with 4G of thrust starting at rest and presuming no outside influences.
Turn 1:
The player decides to move at full thrust. Draw a vector 400mm long in the desired direction (Vector 1). The ship has moved a total of 400mm (40,000km) and is at the terminator of Vector 1.
Turn 2: Option A:
The player does nothing and simply coasts along. Draw a 400mm vector (Vector 2A) in the same direction, starting at the terminator of the previous vector (Vector 1). This is the current vector. The ship has now moved a total of 800mm (80,000km) and is at the terminator of Vector 2A with a current vector of 400mm in the original direction.
Turn 2: Option B:
The player decides to continue on course at full thrust. Draw a 400mm vector (Vector 2B part 1) in the same direction starting at the terminator of the previous vector (Vector 1). This is the current vector. Then draw a 400mm vector (Vector 2B part 2) from that terminus in the same direction (for the current turn of thrust). Connect the tail of Vector 2B part 1 to the terminus of Vector 2B part 2 to complete Vector 2B for a total of a 800mm vector. The ship has moved a total of 1200mm (120,000km) and is at the terminator of Vector 2B with a current vector of 800mm in the original direction.
Turn 2: Option C:
The player decides to apply full thrust in the opposite direction to come to a full stop. Draw a 400mm vector (Vector 2C part 1) in the same direction starting at the terminator of the previous vector (Vector 1). This is the current vector. Then draw a 400mm vector (Vector 2C part 2) but reverse it so the terminus points in the opposite direction (for the current turn of thrust) by putting the terminus of Vector 2C part 2 at the terminus of Vector 2C part 1. Connect the tail of Vector 2C part 1 to the terminus of Vector 2C part 2 to complete Vector 2C for a total of a 400mm vector. The ship has moved a total of 800mm (80,000km) and is at the terminator of Vector 2C with a current vector of zero.
Things get a little more involved with different thrust, changing direction, or introducing gravity effects but it is still just a matter of adding the vectors by connecting origins to terminators.
Vectors are really simple to use once you get the basics. As noted though you don't need them often, and some find them too fiddly to bother with. We used them a couple times in CT and then never again. It was interesting though, and made combat a little more interesting. Give it a try in a couple simple scenarios.
If I've goofed (it's all from memory) and somebody notices speak up. I don't think I goofed but you never know.
