How do I get the 'On A Rail' achievement?

No, you have to travel 1000m (=1000 blocks) from the point where you started in one direction. The rails can go up and down but they have to go a 1000 blocks in one direction.

What I mean is that, you can divert from the path, but you have to have travelled 1000 blocks in one direction.

Let's say there are directions W,X,Y,Z.

W = Forward

X = Backward

Y = Right

Z = Left

Now, if you want to go 1000m in W direction, you can divert and go a bit Y and Z, but they will not be counted, similarly, X will also not be counted. You need to travel 1000 blocks only in W direction.

It does not have to be in a single direction as others have pointed out but you have to end up over 1000 blocks or meters as the crow flies from your starting point.

For example: if you travel 820 blocks west and 550 blocks south this will not work since your end location is 988 blocks from where you began. If you traveled 20 blocks further west you would get the achievement since you are now 1004 blocks from your starting point.